Related papers: Focusing waves in unknown media by modified time r…
We adapt boundary deformation techniques to solve a Neumann problem for the Helmholtz equation with rough electric potentials in bounded domains. In particular, we study the dependance of Neumann eigenvalues of the perturbed Laplacian with…
We deal with two dynamical systems associated with a Riemannian manifold with boundary. The first one is a system governed by the scalar wave equation, the second is governed by the Maxwell equations. Both of the systems are controlled from…
We study the inverse problem of determining both the source of a wave and its speed inside a medium from measurements of the solution of the wave equation on the boundary. This problem arises in photoacoustic and thermoacoustic tomography,…
Given near or far field wave measurements generated by some unknown time- and space-dependent acoustic source, we seek to rapidly determine a domain in space-time, as small as possible, that contains the support of a source radiating these…
We consider a restricted Dirichlet-to-Neumann map associated to a wave type operator on a Riemannian manifold with boundary. The restriction corresponds to the case where the Dirichlet traces are supported on one subset of the boundary and…
We establish the decay of the solutions of the damped wave equations in one dimensional space for the Dirichlet, Neumann, and dynamic boundary conditions where the damping coefficient is a function of space and time. The analysis is based…
In this paper we provide bound estimates for the two fastest wave speeds emerging from the solution of the Riemann problem for three well-known hyperbolic systems, namely the Euler equations of gas dynamics, the shallow water equations and…
In this paper, we treat the inverse problem of determining two time-dependent coefficients appearing in a dissipative wave equation, from measured Neumann boundary observations. We establish in dimension $n\geq 2$, stability estimates with…
We consider the wave equation in a bounded domain (eventually convex). Two kinds of inequality are described when occurs trapped ray. Applications to control theory are given. First, we link such kind of estimate with the damped wave…
We study the reconstruction of the initial pressure $f(x)=p(x,0)$ for the wave model \[ \partial_t^2 p(x,t)=c(x)\Delta_{x}p(x,t)\qquad (x,t)\in\Omega\times[0,\infty), \] posed on a bounded domain $\Omega$ with variable sound speed…
We study Maxwell's equations in time domain in an anisotropic medium. The goal of the paper is to solve an inverse boundary value problem for anisotropies characterized by scalar impedance $\alpha$. This means that the material is…
The time reversal symmetry of the wave equation allows wave refocusing back at the source. However, this symmetry does not hold in lossy media. We present a new strategy to compensate wave amplitude losses due to attenuation. The strategy…
Optimal control of nonlinear acoustic waves is relevant in many medical ultrasound technologies, ranging from cancer therapy to targeted drug delivery, where it can help guide the precise deposition of acoustic energy. In this work, we…
In this article we seek stability estimates in the inverse problem of determining the potential or the velocity in a wave equation in an anisotropic medium from measured Neumann boundary observations. This information is enclosed in the…
This paper concerns an inverse boundary value problem of recovering a zeroth order time-dependent term of a semi-linear wave equation on a globally hyperbolic Lorentzian manifold. We show that an unknown potential $q$ in the non-linear wave…
Let $\Delta_{\Lambda}\le \lambda_{\Lambda}$ be a semi-bounded self-adjoint realization of the Laplace operator with boundary conditions (Dirichlet, Neumann, semi-transparent) assigned on the Lipschitz boundary of a bounded obstacle…
We study the inverse problem for a semilinear wave equation on metric tree graphs. From the Dirichlet-to-Neumann map defined at all but one of the boundary vertices, we recover unknown connectivity of the graph, lengths of the edges, the…
In this paper, we are concerned with the stochastic time-fractional diffusion-wave equations in a Hilbert space. The main objective of this paper is to establish properties of the stochastic weak solutions of the initial-boundary value…
We consider the inverse source problem arising in thermo- and photo-acoustic tomography. It consists in reconstructing the initial pressure from the boundary measurements of the acoustic wave. Our goal is to extend versatile time reversal…
Time reflection and refraction are temporal analogies of the spatial boundary effects derived from Fermat's principle. They occur when classical waves strike a time boundary where an abrupt change in the properties of the medium is…