相关论文: Boundary conditions for coupled quasilinear wave e…

We give a short proof of local well-posedness for the initial boundary value problem in general relativity with sole boundary condition the requirement that the boundary is umbilic. This includes as a special case the totally geodesic…

This paper is concerned with the Klein-Gordon-Maxwell system in a bounded spatial domain. We discuss the existence of standing waves $\psi=u(x)e^{-i\omega t}$ in equilibrium with a purely electrostatic field $\mathbf{E}=-\nabla\phi(x)$. We…

The purpose of this paper is to demonstrate how different types of boundary conditions do not impact the asymptotic behaviour of the solutions of thermoelastic wave model. For an initial-boundary value problem associated with this system,…

This paper investigates an inverse boundary value problem for a semilinear strongly damped wave equation with Dirichlet boundary conditions in Sobolev spaces of functions bounded in time on $\R$, including periodic and almost periodic…

In this paper, we study the initial boundary value problem for the nonlinear wave equation with combined power-type nonlinearities with variable coefficients. The global behavior of the solutions with non-positive and sub-critical energy is…

We consider a quasi-linear parabolic equation with nonlinear dynamic boundary conditions occurring as a natural generalization of the semilinear reaction-diffusion equation with dynamic boundary conditions. The corresponding class of…

We consider initial-boundary problems for general linear first-order strictly hyperbolic systems with local or nonlocal nonlinear boundary conditions. While boundary data are supposed to be smooth, initial conditions can contain…

This brief note wants to bring to attention that the formulation of physically reasonable initial-boundary value problems for wave equations in Lorentzian space-times is not unique, i.e., that there are inequivalent such formulations that…

The principle part of Einstein equations in the harmonic gauge consists of a constrained system of 10 curved space wave equations for the components of the space-time metric. A new formulation of constraint-preserving boundary conditions of…

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 prove global well-posedness of the initial value problem for a class of variational quasilinear wave equations, in one spatial dimension, with initial data that is not-necessarily small. Key to our argument is a form of quasilinear null…

This article is devoted to the proof of the well-posedness of a model describing waves propagating in shallow water in horizontal dimension $d=2$ and in the presence of a fixed partially immersed object. We first show that this…

We analyze the initial value problem for semilinear wave equations on asymptotically anti-de Sitter spaces using energy methods adapted to the geometry of the problem at infinity. The key feature is that the coefficients become strongly…

We consider an initial boundary value problem in a bounded domain $\Omega$ over a time interval $(0, T)$ for a time-fractional wave equation where the order of the fractional time derivative is between $1$ and $2$ and the spatial elliptic…

We introduce a formulation of the initial and boundary value problem for nonlinear hyperbolic conservation laws posed on a differential manifold endowed with a volume form, possibly with a boundary; in particular, this includes the…

We study the rate of convergence for (variational) eigenvalues of several non-linear problems involving oscillating weights and subject to different kinds of boundary conditions in bounded domains.

It is shown that natural boundary conditions for non-relativistic wave functions are of periodic or of homogeneous Robin type. Using asymptotic central symmetry of Hamiltonian and theory of singular differential equations the many-electron…

Motivated by the initial-boundary value problem for the Einstein equations, we propose a definition of symmetric hyperbolicity for systems of evolution equations that are first order in time but second order in space. This can be used to…

Solution of Helmholtz equation with impedance boundary condition on finite interval is equivalently reformulated as steady state of initial boundary value problem for first order hyperbolic system of partial differential equations.…

We propose methods that augment existing numerical schemes for the simulation of hyperbolic balance laws with Dirichlet boundary conditions to allow for the simulation of a broad class of differential algebraic conditions. Our approach is…