Related papers: Singular Klein-Gordon equation on a bounded domain
Given a Hilbert space, we investigate the well-posedness of the Cauchy problem for the wave equation for operators with discrete non-negative spectrum acting on it. We consider the cases when the time-dependent propagation speed is regular,…
This paper deals with the homogenization of a mixed boundary value problem for the Laplace operator in a domain with locally periodic oscillating boundary. The Neumann condition is prescribed on the oscillating part of the boundary, and the…
This paper complements the existing theory developed in [5] for the Dirichlet and Neumann problems for the Laplace equation, in multiply connected domains. Within the framework of layer potential methods, we study the Laplace equation under…
In this paper, we consider an acoustic wave transmission problem with mixed boundary conditions of Dirichlet, Neumann, and impedance type. The transmission interfaces may join the domain boundary in a general way independent of the location…
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…
For a damped wave (or Klein-Gordon) equation on a bounded domain, with a focusing power-like nonlinearity satisfying some growth conditions, we prove that a global solution is bounded in the energy space, uniformly in time. Our result…
In this paper we study a double-phase problem involving the 1-Laplacian with non-homogeneous Dirichlet boundary conditions and show the existence and uniqueness of a solution in a suitable weak sense. We also provide a variational…
We study existence and uniqueness of solutions to a class of nonlinear degenerate parabolic equations, in bounded domains. We show that there exists a unique solution which satisfies possibly inhomogeneous Dirichlet boundary conditions. To…
The purpose of the present paper is to establish appropriate cut-off resolvent estimates for the Dirichlet Laplacian on exterior domains. The geometrical assumptions on domains are rather general, for example, non-trapping condition is not…
The covariant Klein-Gordon equation requires twice the boundary conditions of the Schrodinger equation and does not have an accepted single-particle interpretation. Instead of interpreting its solution as a probability wave determined by an…
In this paper, we consider a weakly coupled system consisting of a viscoelastic Kirchhoff plate equation involving free boundary conditions and the viscoelastic wave equation with Dirichlet boundary conditions in a bounded domain. By…
This article deals with the uniqueness and stability issues in the inverse problem of determining the unbounded potential of the Schr\"odinger operator in a bounded domain of dimension 3 or greater, endowed with Robin boundary condition,…
We study a Klein-Gordon-Maxwell system, in a bounded spatial domain, under Neumann boundary conditions on the electric potential. We allow a nonconstant coupling coefficient. For sufficiently small data, we find infinitely many standing…
We study the Lagrange representation of the wave equation with generalized Laplacian $\operatorname{div} T \nabla$. We allow the coefficients -- the Young modulus $T$ and the density $\rho$ -- to be $\mathrm{L}^{\infty}$ or even nonlocal…
This paper studies an inverse hyperbolic problem for the wave equation with dynamic boundary conditions. It consists of determining some forcing terms from the final overdetermination of the displacement. First, the Fr\'echet…
This paper considers to the problems of diffraction of electromagnetic waves on a half-plane, which has a finite inclusion in the form of a Lipschitz curve. The diffraction problem formulated as boundary value problem for Helmholtz…
In this paper, we consider the Cauchy problem for a non-homogeneous wave equation generated by the fractional Laplacian and involving different kinds of lower order terms. We allow the equation coefficients and data to be of distributional…
There is much discussion in the mathematical physics literature as well as in quantum mechanics textbooks on spherically symmetric potentials. Nevertheless, there is no consensus about the behavior of the radial function at the origin,…
We consider a space-fractional wave equation with a singular mass term depending on the position and prove that it is very weak well-posed. The uniqueness is proved in some appropriate sense. Moreover, we prove the consistency of the very…
In this paper, exploiting variational methods, the existence of three weak solutions for a class of elliptic equations involving a general operator in divergence form and with Dirichlet boundary condition is investigated. Several special…