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Dynamics of Bubbling Wave Maps with Prescribed RadiationAug 22 2019We study energy critical one-equivariant wave maps taking values in the two-sphere. It is known that any finite energy wave map that develops a singularity does so by concentrating the energy of (possibly) several copies of the ground state harmonic map ... More

Some remarks on the asymptotic profile of solutions to structurally damped $σ$-evolution equationsAug 22 2019In this paper, we are interested in analyzing the asymptotic profiles of solutions to the Cauchy problem for linear structurally damped $\sigma$-evolution equations in $L^2$-sense. Depending on the parameters $\sigma$ and $\delta$ we would like to not ... More

Electromagnetic wave scattering from local perturbed periodic inhomogeneous layersAug 22 2019We consider the scattering problem on locally perturbed periodic penetrable dielectric layers, which is formulated in terms of the full vector-valued time-harmonic Maxwell's equations. The right-hand side is not assumed to be periodic. At first, we derive ... More

Optimal unions of scaled copies of domains and Pólya's conjectureAug 22 2019Given a bounded Euclidean domain $\Omega$, we consider the sequence of optimisers of the $k^{\rm th}$ Laplacian eigenvalue within the family consisting of all possible disjoint unions of scaled copies of $\Omega$ with fixed total volume. We show that ... More

Recovery of the Derivative of the Conductivity at the BoundaryAug 22 2019We describe a method to reconstruct the conductivity and its normal derivative at the boundary from the knowledge of the potential and current measured at the boundary. This boundary determination implies the uniqueness of the conductivity in the bulk ... More

Existence and multiplicity results for a new $p(x)$-Kirchhoff problemAug 22 2019We study the existence and multiplicity results for the following nonlocal $p(x)$-Kirchhoff problem: \begin{equation} \label{10} \begin{cases} -\left(a-b\int_\Omega\frac{1}{p(x)}| \nabla u| ^{p(x)}dx\right)div(|\nabla u| ^{p(x)-2}\nabla u)=\lambda |u| ... More

Wave front set of solutions to Schrödinger equations with perturbed harmonic oscillatorsAug 22 2019In this paper, we determine the wave front sets of solutions to Schr\"odinger equations of a harmonic oscillator with sub-quadratic perturbation by using the representation of the Schr\"odinger evolution operator of a harmonic oscillator via the wave ... More

Spatial and Spatiotemporal GARCH Models -- A Unified ApproachAug 22 2019In time-series analyses and particularly in finance, generalised autoregressive conditional heteroscedasticity (GARCH) models are widely applied statistical tools for modelling volatility clusters (i.e. periods of increased or decreased risks). In contrast, ... More

Homogenization of Stokes equations in perforated domains: a unified approachAug 22 2019We consider the homogenization of the Stokes equations in a domain perorated with a large number of small holes which are periodically distributed. In [1,2], Allaire gave a systematic study on this problem. In this paper, we introduce a unified proof ... More

Uniqueness of the solution of nonlinear singular first order partial differential equationsAug 22 2019This paper deals with nonlinear singular partial differential equations of the form $t \partial u/\partial t=F(t,x,u,\partial u/\partial x)$ with independent variables $(t,x) \in \mathbb{R} \times \mathbb{C}$, where $F(t,x,u,v)$ is a function continuous ... More

Supercritical elliptic problems on the round sphere and nodal solutions to the Yamabe problem in projective spacesAug 21 2019Given an isoparametric function $f$ on the $n$-dimensional round sphere, we consider functions of the form $u=w\circ f$ to reduce the semilinear elliptic problem \[ -\Delta_{g_0}u+\lambda u=\lambda\ | u\ | ^{p-1}u\qquad\text{ on }\mathbb{S}^n \] with ... More

Bloch wave approach to almost periodic homogenization and approximations of effective coefficientsAug 21 2019Bloch wave homogenization is a spectral method for obtaining effective coefficients for periodically heterogeneous media. This method hinges on the direct integral decomposition of periodic operators, which is not available in a suitable form for almost ... More

Fractional heat semigroups on metric measure spaces with finite densities and applications to fractional dissipative equationsAug 21 2019Let $(\mathbb M, d,\mu)$ be a metric measure space with upper and lower densities: $$ \begin{cases} |||\mu|||_{\beta}:=\sup_{(x,r)\in \mathbb M\times(0,\infty)} \mu(B(x,r))r^{-\beta}<\infty;\\ |||\mu|||_{\beta^{\star}}:=\inf_{(x,r)\in \mathbb M\times(0,\infty)} ... More

On an optimal potential of Schrödinger operator with prescribed $m$ eigenvalueAug 21 2019The purpose of this paper is twofold: firstly, we present a new type of relationship between inverse problems and nonlinear differential equations. Secondly, we introduce a new type of inverse spectral problem, posed as follows: for a priori given potential ... More

Existence of solutions for a nonlocal type problem in fractional Orlicz Sobolev spacesAug 21 2019In this paper, we investigate the existence of weak solution for a fractional type problems driven by a nonlocal operator of elliptic type in a fractional Orlicz-Sobolev space, with homogeneous Dirichlet boundary conditions. We first extend the fractional ... More

On the Impulsive Implicit $Ψ$--Hilfer Fractional Differential Equations with DelayAug 21 2019In this paper, we investigate the existence and uniqueness of solutions and derive the Ulam--Hyers--Mittag--Leffler stability results for impulsive implicit $\Psi$--Hilfer fractional differential equations with time delay. It is demonstrated that the ... More

Analysis of Impulsive $\varphi$--Hilfer Fractional Differential EquationsAug 21 2019This paper is concerned with the existence and uniqueness, and Ulam--Hyers stabilities of solutions of nonlinear impulsive $\varphi$--Hilfer fractional differential equations. Further, we investigate the dependence of the solution on the initial conditions, ... More

An iterative method for Kirchhoff type equations and its applicationsAug 21 2019In this short note, we propose an iterative method for finding nonnegative solutions of Kirchhoff type equations.

Non-negativity of CR Paneitz operator for embeddable CR manifoldsAug 21 2019The non-negativity of the CR Paneitz operator plays a crucial role in three-dimensional CR geometry. In this paper, we prove this non-negativity for embeddable CR manifolds. This result and previous works give an affirmative solution of the CR Yamabe ... More

On the trend to global equilibrium for Kuramoto OscillatorsAug 21 2019In this paper, we study the convergence to the stable equilibrium for Kuramoto oscillators. Specifically, we derive estimates on the rate of convergence to the global equilibrium for solutions of the Kuramoto-Sakaguchi equation in a large coupling strength ... More

Heat kernel estimates and parabolic Harnack inequalities for symmetric Dirichlet formsAug 20 2019In this paper, we consider the following symmetric Dirichlet forms on a metric measure space $(M,d,\mu)$: $$\mathcal{E}(f,g) = \mathcal{E}(^{(c)}(f,g)+\int_{M\times M} (f(x)-f(y))(g(x)-g(y))\,J(dx,dy),$$ where $\mathcal{E}(^{(c)}$ is a strongly local ... More

Classic dynamic fracture recovered as the limit of a nonlocal peridynamic model: The single edge notch in tensionAug 20 2019A simple nonlocal field theory of peridynamic type is applied to model brittle fracture. The fracture evolution is shown to converge in the limit of vanishing nonlocality to classic plane elastodynamics with a running crack. The kinetic relation for the ... More

On the well-posedness, ill-posedness and norm-inflation for a higher order water wave model on a periodic domainAug 20 2019In this work we are interested in the well-posedness issues for the initial value problem associated with a higher order water wave model posed on a pe\-rio\-dic domain $\mathbb{T}$. We derive some multilinear estimates and use them in the contraction ... More

Boundary spike-layer solutions of the singular Keller-Segel system: existence and stabilityAug 20 2019We exploit the existence and nonlinear stability of boundary spike/layer solutions of the Keller-Segel system with logarithmic singular sensitivity in the half space, where the physical zero-flux and Dirichlet boundary conditions are prescribed. We first ... More

The global well-posedness for the compressible fluid model of Korteweg typeAug 20 2019In this paper, we consider the compressible fluid model of Korteweg type which can be used as a phase transition model. It is shown that the system admits a unique, global strong solution for small initial data in $\mathbb R^N$, $N \geq 3$. In this study, ... More

Fundamental solutions of the generalized Helmholtz equation with several singular coefficients and confluent hypergeometric functions of many variablesAug 20 2019In this paper, we introduce a new class of confluent hypergeometric functions of many variables, study their properties, and determine a system of partial differential equations that this function satisfies. It turns out that all the fundamental solutions ... More

Well-posedness of the Fractional Porous Medium Equation on Manifolds with Conical SingularitiesAug 20 2019In this article, we consider the fractional porous medium equation, $\partial_t u +(-\Delta)^\sigma (|u|^{m-1}u )=0 $, posed on a Riemannian manifold with isolated conical singularities, with $m>0$ and $\sigma\in (0,1]$. For $L_\infty-$initial data, we ... More

Existence of multiple solutions for quasi-linear degenerate elliptic equationsAug 20 2019The present paper is concerned a class of quasi-linear elliptic degenerate equations. The degenerate operator comes from the analysis of manifolds with corner singularity. Variational methods are applied to verify the existence of infinity many solutions ... More

Blow-up and strong instability of standing waves for the NLS-$δ$ equation on a star graphAug 20 2019We study strong instability (by blow-up) of the standing waves for the nonlinear Schr\"odinger equation with $\delta$-interaction on a star graph $\Gamma$. The key ingredient is a novel variational technique applied to the standing wave solutions being ... More

The IVP for a higher dimensional version of the Benjamin-Ono equation in weighted Sobolev spacesAug 19 2019We study the initial value problem associated to a higher dimensional version of the Benjamin-Ono equation. Our purpose is to establish local well-posedness results in weighted Sobolev spaces and to determinate according to them some sharp unique continuation ... More

The fractional porous medium equation on manifolds with conical singularitiesAug 19 2019We show $R$-sectoriality for the fractional powers of possibly non-invertible $R$-sectorial operators. Applications concern existence, uniqueness and maximal $L^{q}$-regularity results for solutions of the fractional porous medium equation on manifolds ... More

When do cross-diffusion systems have an entropy structure?Aug 19 2019Necessary and sufficient conditions for the existence of an entropy structure for certain classes of cross-diffusion systems with diffusion matrix $A(u)$ are derived, based on results from matrix factorization. The entropy structure is important in the ... More

On symmetry and uniqueness of ground states for linear and nonlinear elliptic PDEsAug 19 2019We study ground state solutions for linear and nonlinear elliptic PDEs in $\mathbb{R}^n$ with (pseudo-)differential operators of arbitrary order. We prove a general symmetry result in the nonlinear case as well as a uniqueness result for ground states ... More

On symmetry of traveling solitary waves for dispersion generalized NLSAug 19 2019We consider dispersion generalized nonlinear Schr\"odinger equations (NLS) of the form $i \partial_t u = P(D) u - |u|^{2 \sigma} u$, where $P(D)$ denotes a (pseudo)-differential operator of arbitrary order. As a main result, we prove symmetry results ... More

A simple proof of the Hardy inequality on Carnot groups and for some hypoelliptic families of vector fieldsAug 19 2019We give an elementary proof of the classical Hardy inequality on any Carnot group, using only integration by parts and a fine analysis of the commutator structure, which was not deemed possible until now. We also discuss the conditions under which this ... More

Global continuity and higher integrability of a minimizer of an obstacle problem under generalized Orlicz growth conditionsAug 19 2019We prove continuity up to the boundary of the minimizer of an obstacle problem and higher integrability of its gradient under generalized Orlicz growth. The result recovers similar results obtained in the special cases of polynomial growth, variable exponent ... More

The Dirichlet problem for a prescribed mean curvature equationAug 19 2019We study a prescribed mean curvature problem where we seek a surface whose mean curvature vector coincides with the normal component of a given vector field. We prove that the problem has a solution near a graphical minimal surface if the prescribed vector ... More

Inverse source problems in transport via attenuated tensor tomographyAug 18 2019We establish results for the injectivity and injectivity modulo gauge of certain inverse source problems in transport on a simply connected domain with variable index of refraction inducing a 'simple geometry'. The model given by radiative transfer involves ... More

Uniform attractors of non-autonomous Kirchhoff wave modelsAug 18 2019The paper investigates the existence and upper semicontinuity of uniform attractors of the perturbed non-autonomous Kirchhoff wave equations with strong damping and supercritical nonlinearity: $u_{tt}-\Delta u_{t}-(1+\epsilon\|\nabla u\|^{2})\Delta u+f(u)=g(x,t)$, ... More

The selection problem for some first-order stationary mean-field gamesAug 18 2019Here, we study the existence and the convergence of solutions for the vanishing discount MFG problem with a quadratic Hamiltonian. We give conditions under which the discounted problem has a unique classical solution and prove convergence of the vanishing-discount ... More

Bifurcation for Minimal Surface Equation in Hyperbolic $3$-ManifoldsAug 18 2019Initiated by the work of Uhlenbeck in late 1970s, we study questions about the existence, multiplicity and asymptotic behavior for minimal immersions of closed surface in some hyperbolic three-manifold, with prescribed conformal structure on the surface ... More

Sloshing, Steklov and corners: Asymptotics of Steklov eigenvalues for curvilinear polygonsAug 18 2019We obtain asymptotic formulae for the Steklov eigenvalues and eigenfunctions of curvilinear polygons in terms of their side lengths and angles. These formulae are quite precise: the errors tend to zero as the spectral parameter tends to infinity. The ... More

Long-time asymptotics for the integrable nonlocal focusing nonlinear Schrödinger equation for a family of step-like initial dataAug 18 2019We study the Cauchy problem for the integrable nonlocal focusing nonlinear Schr\"odinger (NNLS) equation $ iq_{t}(x,t)+q_{xx}(x,t)+2 q^{2}(x,t)\bar{q}(-x,t)=0 $ with the step-like initial data close to the ``shifted step function'' $\chi_R(x)=AH(x-R)$, ... More

On a thin film model with insoluble surfactantAug 18 2019Aug 20 2019This paper studies the existence and asymptotic behavior of global weak solutions for a thin film equation with insoluble surfactant under the influence of gravitational, capillary and van der Waals forces. We prove the existence of global weak solutions ... More

On a thin film model with insoluble surfactantAug 18 2019This paper studies the existence and asymptotic behavior of global weak solutions for a thin film equation with insoluble surfactant under the influence of gravitational, capillary and van der Waals forces. We prove the existence of global weak solutions ... More

Global Regularity for minimal graphs over convex domains in hyperbolic spaceAug 18 2019In this paper we study the global regularity for the solution to the Dirichlet problem of the equation of minimal graphs over a convex domain in hyperbolic spaces. We find that the global regularity depends only on the convexity of the domain but independent ... More

On A Class of Degenerate And Singular Monge-Ampère EquationsAug 18 2019In this paper we shall prove the existence, uniqueness and global H$\ddot{o}$lder continuity for the Dirichlet problem of a class of Monge-Amp\`ere type equations which may be degenerate and singular on the boundary of convex domains. We will establish ... More

Invariant parameterization of geostrophic eddies in the oceanAug 17 2019The framework of invariant parameterization is extended to higher-order closure schemes. We also define, for the first time, generalized invariant parameterization schemes, where symmetries of the corresponding original model are preserved as equivalence ... More

Optimal Trapping of Brownian Motion: A Nonlinear Analogue of the Torsion FunctionAug 17 2019We study the problem of maximizing the expected lifetime of drift diffusion in a bounded domain. More formally, we consider the PDE \[ - \Delta u + b(x) \cdot \nabla u = 1 \qquad \mbox{in}~\Omega\] subject to Dirichlet boundary conditions for $\|b\|_{L^{\infty}}$ ... More

Generalized potential gamesAug 17 2019In this paper, we introduce a notion of generalized potential games that is inspired by a newly developed theory on generalized gradient flows. More precisely, a game is called generalized potential if the simultaneous gradient of the loss functions is ... More

Exponential integrability in the spirit of Moser-Trudinger's inequalities of functions with finite non-local, non-convex energyAug 16 2019Let $d \ge 1$, $p \ge d$, and let $\Omega$ be a smooth bounded open subset of $\mathbb{R}^d$. We prove some exponential integrability in the spirit of Moser-Trudinger's inequalities for measurable functions $u$ defined in $\Omega$ such that $$ \mathop{\int_{\Omega} ... More

Convergence of a Robin boundary approximation for a Cahn--Hilliard system with dynamic boundary conditionsAug 16 2019We prove the existence of unique weak solutions to an extension of a Cahn--Hilliard model proposed recently by C.~Liu and H.~Wu (2019), in which the new dynamic boundary condition is further generalised with an affine linear relation between the surface ... More

On the eigenvalues of the Robin Laplacian with a complex parameterAug 16 2019We study the spectrum of the Robin Laplacian with a complex Robin parameter $\alpha$ on a bounded Lipschitz domain $\Omega$. We start by establishing a number of properties of the corresponding operator, such as generation properties, local analytic dependence ... More

Some hemivariational inequalities in the Euclidean spaceAug 16 2019The purpose of this paper is to study the existence of weak solutions for some classes of hemivariational problems in the Euclidean space $\mathbb{R}^d$ ($d\geq 3$). These hemivariational inequalities have a variational structure and, thanks to this, ... More

Stability Results for the Continuity EquationAug 16 2019We provide a thorough study of stability of the 1-D continuity equation, which models many physical conservation laws. In our system-theoretic perspective, the velocity is considered to be an input. An additional input appears in the boundary condition ... More

The Heintze-Karcher inequality for sets of finite perimeter and bounded mean curvatureAug 16 2019We establish the Heintze-Karcher inequality for sets of finite perimeter and bounded generalized mean curvature (in the sense of varifold's theory) and we prove that the equality case is uniquely characterized by finite unions of disjoint open balls.

Stochastic Comparisons of Series and Parallel Systems with Topp-Leone Generated Family of DistributionsAug 16 2019In this article, we stochastically compare the series and parallel systems having Topp Leone generated family of distributions. We consider that the lifetimes of the components of the systems have either the different shape parameters when the scale parameters ... More

Homogenization of linear parabolic equations with three spatial and three temporal scales for certain matchings between the microscopic scalesAug 16 2019In this paper we establish compactness results of multiscale and very weak multiscale type for sequences bounded in $L^{2}(0,T;H_{0}^{1}(\Omega ))$, fulfilling a certain condition. We apply the results in the homogenization of the parabolic partial differential ... More

The Defocusing Energy-critical Klein-Gordon-Hartree EquationAug 16 2019In this paper, we study the scattering theory for the defocusing energy-critical Klein-Gordon equation with a cubic convolution $u_{tt}-\Delta u+u+(|x|^{-4}\ast|u|^2)u=0$ in the spatial dimension $d \geq 5$. We utilize the strategy in [S. Ibrahim, N. ... More

Unique continuation for a non bi-Laplacian fourth order elliptic operatorAug 16 2019This paper discusses the unique continuation principal of the solutions of the following perturbed fourth order elliptic differential operator $\mathcal{L}_{A,q}u=0$, where \[ \mathcal{L}_{A,q}(x,D)\ =\ \sum_{j=1}^nD^4_{x_j} + \sum_{j=1}^n A_jD_{x_j} ... More

The Hartree-Fock equations in modulation spacesAug 16 2019We establish both a local and a global well-posedness theories for the nonlinear Hartree-Fock equations and its reduced analog in the setting of the modulation spaces on $\mathbb R^d$. In addition, we prove similar results when a harmonic potential is ... More

On the inverse scattering from anisotropic periodic layers and transmission eigenvaluesAug 16 2019This paper is concerned with the inverse scattering and the transmission eigenvalues for anisotropic periodic layers. For the inverse scattering problem, we study the Factorization method for shape reconstruction of the periodic layers from near field ... More

The Direct and Generalized Linear Sampling Methods for Maxwell's EquationsAug 16 2019This paper is concerned with the inverse scattering problem that aims to determine the shape of electromagnetic scatterers from far-field data (at a fixed frequency). We investigate the direct and generalized linear sampling methods for solving this electromagnetic ... More

Analysis of the spectral symbol function for spectral approximation of a differential operatorAug 15 2019Given a differential operator $\mathcal{L}$ along with its own eigenvalue problem $\mathcal{L}u = \lambda u$ and an associated algebraic equation $\mathcal{L}^{(n)} \mathbf{u}_n = \lambda\mathbf{u}_n$ obtained by means of a discretization scheme (like ... More

Blow-up solutions to 3D Euler are hydrodynamically unstableAug 15 2019We study the interaction between the stability, and the propagation of regularity, for solutions to the incompressible 3D Euler equation. It is still unknown whether a solution with smooth initial data can develop a singularity in finite time. This article ... More

Isotonic regression discontinuity designsAug 15 2019In isotonic regression discontinuity designs, the average outcome and the treatment assignment probability are monotone in the running variable. We introduce novel nonparametric estimators for sharp and fuzzy designs based on the bandwidth-free isotonic ... More

On a Fractional Schrödinger equation in the presence of Harmonic potentialAug 15 2019In this paper, we establish the existence of ground state solutions for a fractional Schr\"odinger equation in the presence of a harmonic trapping potential. We also address the orbital stability of standing waves. Additionally, we obtain novel and interesting ... More

Almost optimal local well-posedness for the Maxwell-Klein-Gordon system with data in Fourier-Lebesgue spacesAug 15 2019We prove a low regularity local well-posedness result for the Maxwell-Klein-Gordon system in three space dimensions for data in Fourier - Lebesgue spaces $\widehat{H}^{s,r}$ , where $\|f\|_{\widehat{H}^{s,r}} = \|\langle \xi \rangle^s \widehat{f}(\xi)\|_{\widehat{L}^{r'}}$ ... More

An Improved Compact Embedding Theorem for Degenerate Sobolev SpacesAug 15 2019This short note investigates the compact embedding of degenerate matrix weighted Sobolev spaces into weighted Lebesgue spaces. The Sobolev spaces explored are defined as the abstract completion of Lipschitz functions in a bounded domain $\Omega$ with ... More

Sharp polynomial decay rates for the damped wave equation with Hölder-like dampingAug 15 2019We study decay rates for the energy of solutions of the damped wave equation on the torus. We consider dampings invariant in one direction and bounded above and below by multiples of $x^{\beta}$ near the boundary of the support and show decay at rate ... More

Almost scalar-flat Kähler metrics on affine algebraic manifoldsAug 15 2019In this paper, we study the existence of a complete K\"{a}hler metric whose scalar curvature is flat away from some ample divisor and arbitrarily small near it on certain affine algebraic manifold. Such a metric is obtained by gluing the solution of the ... More

Sharp estimates for spreading speed of the Lotka-Volterra diffusion system with strong competitionAug 15 2019This paper concerns the classical two-species Lotka-Volterra diffusion system with strong competition. The sharp dynamical behavior of the solution is established in two different situations: either one species is an invasive one and the other is a native ... More

Bubbling solutions for a planar exponential nonlinear elliptic equation with a singular sourceAug 15 2019Aug 21 2019Let $\Omega$ be a bounded domain in $\mathbb{R}^2$ with smooth boundary, we study the following elliptic Dirichlet problem $$ \begin{cases} -\Delta\upsilon= e^{\upsilon}-s\phi_1-4\pi\alpha\delta_p-h(x)\,\,\,\, \,\textrm{in}\,\,\,\,\,\Omega,\\[2mm] \upsilon=0 ... More

Bubbling solutions for a planar exponential nonlinear elliptic equation with a singular sourceAug 15 2019Let $\Omega$ be a bounded domain in $\mathbb{R}^2$ with smooth boundary, we study the following elliptic Dirichlet problem \begin{equation*} \aligned \left\{\aligned &-\Delta\upsilon= e^{\upsilon}-s\phi_1-4\pi\alpha\delta_p-h(x)\,\,\,\, \,\textrm{in}\,\,\,\,\,\Omega,\\[2mm] ... More

Bubbling solutions for a planar exponential nonlinear elliptic equation with a singular sourceAug 15 2019Aug 20 2019Let $\Omega$ be a bounded domain in $\mathbb{R}^2$ with smooth boundary, we study the following elliptic Dirichlet problem $$ \begin{cases} -\Delta\upsilon= e^{\upsilon}-s\phi_1-4\pi\alpha\delta_p-h(x)\,\,\,\, \,\textrm{in}\,\,\,\,\,\Omega,\\[2mm] \upsilon=0 ... More

Bubbling solutions for a planar exponential nonlinear elliptic equation with a singular sourceAug 15 2019Aug 16 2019Let $\Omega$ be a bounded domain in $\mathbb{R}^2$ with smooth boundary, we study the following elliptic Dirichlet problem $$ \aligned \left\{\aligned &-\Delta\upsilon= e^{\upsilon}-s\phi_1-4\pi\alpha\delta_p-h(x)\,\,\,\, \,\textrm{in}\,\,\,\,\,\Omega,\\[2mm] ... More

Exponential Attractor for Hindmarsh-Rose Equations in NeurodynamicsAug 14 2019The existence of an exponential attractor for the diffusive Hindmarsh-Rose equations on a three-dimensional bounded domain originated in the study of neurodynamics is proved through uniform estimates together with a new theorem on the squeezing property ... More

Stability Analysis of a Bulk-Surface Reaction Model for Membrane-Protein ClusteringAug 14 2019Protein aggregation on the plasma membrane (PM) is of critical importance to many cellular processes such as cell adhesion, endocytosis, fibrillar conformation, and vesicle transport. Lateral diffusion of protein aggregates or clusters on the surface ... More

Determination of isometric real-analytic metric and spectral invariants for elastic Dirichlet-to-Neumann map on Riemannian manifoldsAug 14 2019For a compact Riemannian manifold $(\Omega, g)$ with smooth boundary $\partial \Omega$, we explicitly give local representation and full symbol expression for the elastic Dirichlet-to-Neumann map $\Xi_g$ by factorizing an equivalent elastic equation. ... More

A minimization problem involving a fractional Hardy-Sobolev type inequalityAug 14 2019In this work, we obtain existence results for a minimization problem involving a fractional Hardy-Sobolev type inequality. Precisely, let $0<s<1, n>4s, 0<\alpha<2s$, and $\Omega \subset \mathbb{R}^n$ be a bounded domain. We find a critical values $0<\lambda_*<\lambda^*$ ... More

Spectral properties of Neumann-Poincare operator and anomalous localized resonance in elasticity beyond quasi-static limitAug 14 2019This paper is concerned with the polariton resonances and their application for cloaking due to anomalous localized resonance (CALR) for the elastic system within the finite frequency regime beyond the quasi-static approximation. We first derive the complete ... More

Spectral properties of Neumann-Poincare operator and anomalous localized resonance in elasticity beyond quasi-static limitAug 14 2019Aug 17 2019This paper is concerned with the polariton resonances and their application for cloaking due to anomalous localized resonance (CALR) for the elastic system within the finite frequency regime beyond the quasi-static approximation. We first derive the complete ... More

Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial dataAug 14 2019Aug 15 2019This is part two of our study on the spreading properties of the Lotka-Volterra competition-diffusion systems with a stable coexistence state. We focus on the case when the initial data are exponential decaying. By establishing a comparison principle ... More

Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial dataAug 14 2019This is part two of our study on the spreading properties of the weak Lotka-Volterra competition-diffusion systems with a stable coexistence state. Here we focus on the case when the initial data are exponential decaying. By the geometric optics approach ... More

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approachAug 14 2019We establish spreading properties of the Lotka-Volterra competition-diffusion system. When the initial data vanish on a right half-line, we derive the exact spreading speeds and prove the convergence to homogeneous equilibrium states between successive ... More

Quantitative bounds for critically bounded solutions to the Navier-Stokes equationsAug 14 2019We revisit the regularity theory of Escauriaza, Seregin, and \v{S}ver\'ak for solutions to the three-dimensional Navier-Stokes equations which are uniformly bounded in the critical $L^3_x(\mathbf{R}^3)$ norm. By replacing all invocations of compactness ... More

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzlesAug 14 2019We establish the stability of 3-D axisymmetric transonic shock solutions of the steady full Euler system in divergent nozzles under small perturbations of an incoming radial supersonic flow and a constant pressure at the exit of the nozzles. To study ... More

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzlesAug 14 2019Aug 15 2019We establish the stability of 3-D axisymmetric transonic shock solutions of the steady full Euler system in divergent nozzles under small perturbations of an incoming radial supersonic flow and a constant pressure at the exit of the nozzles. To study ... More

Determining wavenumbers for the incompressible Hall-magneto-hydrodynamicsAug 13 2019Using Littlewood-Paley theory, one formulates the determining wavenumbers for the Hall-MHD system, defined for each individual solution $(u,b)$. It is shown that the long time behaviour of strong solutions is almost finite dimensional as the wavenumbers ... More

Existence and asymptotics of nonlinear Helmholtz eigenfunctionsAug 13 2019We prove the existence and asymptotic expansion of a large class of solutions to nonlinear Helmholtz equations of the form \begin{equation*} (\Delta - \lambda^2) u = N[u], \end{equation*} where $\Delta = -\sum_j \partial^2_j$ is the Laplacian on $\mathbb{R}^n$ ... More

Invariant Measures for Nonlinear Conservation Laws Driven by Stochastic ForcingAug 13 2019We survey some recent developments in the analysis of the long-time behavior of stochastic solutions of nonlinear conservation laws driven by stochastic forcing. Moreover, we establish the existence and uniqueness of invariant measures for anisotropic ... More

Rigidity for perimeter inequality under spherical symmetrisationAug 13 2019Necessary and sufficient conditions for rigidity of the perimeter inequality under spherical symmetrisation are given. That is, a characterisation for the uniqueness (up to orthogonal transformations) of the extremals is provided. This is obtained through ... More

Superfast amplification and superfast nonlinear saturation of perturbations as the mechanism of turbulenceAug 13 2019Ruelle predicted that the maximal amplification of perturbations in homogeneous isotropic turbulence is exponential $e^{\sigma \sqrt{Re} t}$ (where $\sigma \sqrt{Re}$ is the maximal Liapunov exponent). In our earlier works, we predicted that the maximal ... More

Exponential Decay and Lack of Analyticity for the System of the Kirchhoff Love Plates and Membrane Like Electric Network Equation with Fractional Partial DampingAug 13 2019The emphasis in this paper is on the Coupled System of a Kirchhoff Love Plate Equation with the Equation of a Membrane like Electrical Network, where the coupling is of higher order given by the Laplacian of the displacement velocity $-\gamma\Delta u_t$ ... More

Blow-up phenomena for the constant scalar curvature and constant boundary mean curvature equationAug 13 2019We first present a warped product manifold with boundary to show the non-uniqueness of the positive constant scalar curvature and positive constant boundary mean curvature equation. Next, we construct a smooth counterexample to show that the compactness ... More

Dynamics of Riemann waves with sharp measure-controlled dampingAug 13 2019This paper is concerned with locally damped semilinear wave equations defined on compact Riemannian manifolds with boundary. We present a construction of measure-controlled damping regions which are sharp in the sense that their summed interior and boundary ... More

On explicit $L^2$-convergence rate estimate for underdamped Langevin dynamicsAug 13 2019We provide a new explicit estimate of exponential decay rate of underdamped Langevin dynamics in $L^2$ distance. To achieve this, we first prove a Poincar\'{e}-type inequality with Gibbs measure in space and Gaussian measure in momentum. Our new estimate ... More

Time-changed Dirac-Fokker-Planck equations on the latticeAug 13 2019A time-changed discretization for the Dirac equation is proposed. More precisely, we consider a Dirac equation with discrete space and continuous time perturbed by a time-dependent diffusion term $\sigma^2Ht^{2H-1}$ that resembles to a latticizing version ... More

Bounded geometry and $p$-harmonic functions under uniformization and hyperbolizationAug 13 2019The uniformization and hyperbolization transformations formulated by Bonk, Heinonen and Koskela in \emph{"Uniformizing Gromov Hyperbolic Spaces"}, Ast\'erisque {\bf 270} (2001), dealt with geometric properties of metric spaces. In this paper we consider ... More

Growth of Common Friends in a Preferential Attachment ModelAug 13 2019The number of common friends (or connections) in a graph is a commonly used measure of proximity between two nodes. Such measures are used in link prediction algorithms and recommendation systems in large online social networks. We obtain the rate of ... More