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We consider Schr\"{o}dinger equations with linearly energy-depending potentials which are compactly supported on the half-line. We first provide estimates of the number of eigenvalues and resonances for such complex-valued potentials under…
A method for solving the half-space Sommerfeld problem is proposed, which allows us to obtain exact solutions in the form of Sommerfeld integrals, as well as their short-wave asymptotics. The first carried out by reducing the Sommerfeld…
A method for solving model nonlinear equations describing plasma oscillations in the presence of viscosity and resistivity is given. By first going to the Lagrangian variables and then transforming the space variable conveniently, the…
We consider an isotropic elastic medium occupying a bounded domain D whose density and Lam\'e parameters are piecewise smooth. In the elastic wave initial value inverse problem, we are given the solution operator for the elastic wave…
An inverse problem of wave propagation into a weakly laterally inhomogeneous medium occupying a half-space is considered in the acoustic approximation. The half-space consists of an upper layer and a semi-infinite bottom separated with an…
We study spherically symmetric solutions of semilinear wave equations in the case where the nonlinearity satisfies the null condition on extremal Reissner--Nordstrom black hole spacetimes. We show that solutions which arise from…
We study the inverse problem of recovery a compactly supported non-linearity in the semilinear wave equation $u_{tt}-\Delta u+ \alpha(x) |u|^2u=0$, in two and three dimensions. We probe the medium with complex-valued harmonic waves of…
We consider the logarithmic Schr{\"o}dinger equations with damping, also called Schr{\"o}dinger-Langevin equation. On a periodic domain, this equation possesses plane wave solutions that are explicit. We prove that these solutions are…
This paper is concerned with the resolution of an inverse problem related to the recovery of a scalar (potential) function $V$ from the source to solution map, of the semi-linear equation $(\Box_{g}+V)u+u^3=0$ on a globally hyperbolic…
This paper studies the third boundary problem of the Laplace equation with azimuthal symmetry.Many solutions of the boundary value problems in spherical coordinates are available in the form of infinite series of Legendre polynomials but…
In this article, we report on an exact closed-form solution for the displacement in an elastic homogeneous half-space elicited by a downward vertical point source moving with constant velocity over the surface of the medium. The problem…
We consider an inverse problem of recovering a potential associated to a semi-linear wave equation with a quadratic nonlinearity in $1 + 1$ dimensions. We develop a numerical scheme to determine the potential from a noisy…
In this paper, we investigate an inverse random source problem concerned with recovering the strength of a random, uncorrelated acoustic source from correlation measurements of emitted time-harmonic acoustic waves. Such problems arise in…
We study the problem of recovering the initial data of the two dimensional wave equation from values of its solution on the boundary $\partial \Om$ of a smooth convex bounded domain $\Om \subset \R^2$. As a main result we establish…
This paper concerns an inverse elastic scattering problem which is to determine the location and the shape of a rigid obstacle from the phased or phaseless far-field data for a single incident plane wave. By introducing the Helmholtz…
We study the inverse boundary value problem for the linear elastic wave equation in three-dimensional isotropic medium. We show that both the Lam\'e parameters and the density can be uniquely recovered from the boundary measurements under…
In this work we present a semi-classical approach to solve the inverse spectrum problem for one-dimensional wave equations for a specific class of potentials that admits quasi-stationary states. We show how inverse methods for potential…
We propose a numerical method to solve an inverse source problem of computing the initial condition of hyperbolic equations from the measurements of Cauchy data. This problem arises in thermo- and photo- acoustic tomography in a bounded…
Consider the two-dimensional inverse elastic wave scattering by an infinite rough surface with a Dirichlet boundary condition. A non-interative sampling technique is proposed for detecting the rough surface by taking elastic wave…
Consider an isotropic elastic medium $\Omega \subset \mathbb{R}^3$ whose Lam\'e parameters are piecewise smooth. In the elastic wave initial value inverse problem, we are given the solution operator for the elastic wave equation, but only…