相关论文: A multi-scale Gaussian beam parametrix for the wav…

We derive new, explicit representations for the solution to the scalar wave equation in the exterior of a sphere, subject to either Dirichlet or Robin boundary conditions. Our formula leads to a stable and high-order numerical scheme that…

A fairly general expression for a light beam is found as a solution of the paraxial Helmholtz equation. It is achieved by exploiting appropriately chosen complex variables which entail the separability of the equation. Next, the expression…

We establish two-sided Gaussian bounds for fundamental solutions of general non-divergence form parabolic operators with H\"older continuous coefficients. The result we obtain is essentially based on parametrix method.

We consider the initial boundary value problem for free-evolution formulations of general relativity coupled to a parametrized family of coordinate conditions that includes both the moving puncture and harmonic gauges. We concentrate…

This technical note is a complement to an earlier paper [Benzoni-Gavage \& Rosini, Comput. Math. Appl. 2009], which aims at a deeper understanding of a basic model for propagating phase boundaries that was proved to admit surface waves…

We consider the stability in the inverse problem consisting of the determination of a time-dependent coefficient of order zero $q$, appearing in a Dirichlet initial-boundary value problem for a wave equation $\partial_t^2u-\Delta…

We study the weakly stable hyperbolic boundary value problem with a large zero order oscillatory coefficient. This problem is related to linearized problems in the study of Mach stem and vortex sheets. We wish to establish a uniform energy…

We propose a boundary integral formulation for the dynamic problem of electromagnetic scattering and transmission by homogeneous dielectric obstacles. In the spirit of Costabel and Stephan, we use the transmission conditions to reduce the…

The solutions of boundary value problems for the Laplacian and the bilaplacian exhibit very different qualitative behaviors. Particularly, the failure of general maximum principles for the bilaplacian implies that solutions of higher-order…

It is known that von Neumann-Landau wave equation can present a mathematical formalism of motion of quantum mechanics, that is an extension of Schr\"{o}dinger's wave equation. In this paper, we concern with the Dirichlet problem of the…

We prove the existence of a fundamental solution of the Cauchy initial boundary value problem on the whole space for a parabolic partial differential equation with discontinuous unbounded first-order coefficient at the origin. We establish…

We consider solving the exterior Dirichlet problem for the Helmholtz equation with the $h$-version of the boundary element method (BEM) using the standard second-kind combined-field integral equations. We prove a new, sharp bound on how the…

For the 3-D quadratic quasilinear wave equations in exterior domains with Dirichlet or Neumann boundary conditions, the global existence or the maximal existence time of small data smooth solutions have been established in the past.…

We consider a Dirichlet problem of the $H$-system \begin{equation*} \begin{cases} \Delta v = 2v_x\wedge v_y ~& \text{ in }\mathcal{D},\\ v=\varepsilon \tilde g ~& \text{ on }\partial{\mathcal{D}}, \end{cases} \end{equation*} where $\mathcal…

We consider an inverse problem for a hyperbolic partial differential equation on a compact Riemannian manifold. Assuming that $\Gamma_1$ and $\Gamma_2$ are two disjoint open subsets of the boundary of the manifold we define the restricted…

We show existence and uniqueness for a linearized water wave problem in a two dimensional domain $G$ with corner, formed by two semi-axis $\Gamma_1$ and $\Gamma_2$ which intersect under an angle $\alpha\in (0,\pi ]$. The existence and…

A two-parameter singularly perturbed problem with discontinuous source and convection coefficient is considered in one dimension. Both convection coefficient and source term are discontinuous at a point in the domain. The presence of…

The global existence of strong solution to the initial-boundary value problem of the three-dimensional compressible viscoelastic fluids near equilibrium is established in a bounded domain. Uniform estimates in $W^{1,q}$ with $q>3$ on the…

In this paper we set forth new exact analytical Superluminal localized solutions to the wave equation for arbitrary frequencies and adjustable bandwidth. The formulation presented here is rather simple, and its results can be expressed in…

We prove the existence and uniqueness of a viscosity solution of the parabolic variational inequality with a nonlinear multivalued Neumann-Dirichlet boundary condition:% {equation*} \{{array}{r} \dfrac{\partial u(t,x)}{\partial…