Related papers: One dimensional inverse problem in photoacoustic. …
We consider the Bayesian approach to the inverse problem of recovering the shape of an object from measurements of its scattered acoustic field. Working in the time-harmonic setting, we focus on a Helmholtz transmission problem and then…
This paper deals with the inverse problem of recovering an arbitrary number of fractional damping terms in a wave equation. We develop several approaches on uniqueness and reconstruction, some of them relying on Tauberian theorems on the…
This paper proposes a new fast and stable algorithm for the reconstruction of the plasma boundary from discrete magnetic measurements taken at several locations surrounding the vacuum vessel. The resolution of this inverse problem takes two…
To obtain the initial pressure from the collected data on a planar sensor arrangement in Photoacoustic tomography, there exists an exact analytic frequency domain reconstruction formula. An efficient realization of this formula needs to…
In this paper, we study two types of inverse problems for space semi-discrete stochastic parabolic equations in arbitrary dimensions. The first problem concerns a semi-discrete inverse source problem, which involves determining the random…
In this article, we study several reconstruction methods for the inverse source problem of photoacoustic tomography (PAT) with spatially variable sound speed and damping. The backbone of these methods is the adjoint operators, which we…
This paper is concerned with the analysis of the Cauchy problem of a general class of two-dimensional nonlinear nonlocal wave equations governing anti-plane shear motions in nonlocal elasticity. The nonlocal nature of the problem is…
This paper is concerned with the inverse scattering problem by an unbounded rough surface. A direct imaging method is proposed to reconstruct the rough surface from the scattered near-field Cauchy data generating by point sources and…
The theory of weak solutions for nonlinear conservation laws is now well developed in the case of scalar equations [3] and for one-dimensional hyperbolic systems [1, 2]. For systems in several space dimensions, however, even the global…
In this paper, we address the existence of global solutions to the Cauchy problem of the modified Camassa-Holm (mCH) equation, which is known as a model for the unidirectional propagation of shallow water waves. Based on the spectral…
We discuss the Cauchy problem for anisotropic wave equations. Precisely, we address the question to know which kind of Cauchy data on the lateral boundary are necessary to guarantee the uniqueness of continuation of solutions of an…
We consider the Cauchy problem for the wave equation in the whole space, R^n, with initial data which are distributions supported on finite sets. The main result is a precise description of the geometry of the sets of stationary points of…
In this paper we study the global existence of small data solutions to the Cauchy problem for the semilinear wave equation with scale-invariant damping. We obtain estimates for the solution and its energy with the same decay rate of the…
In this paper, we study the viscous Boussinesq equation in the whole space $\mathbb{R}^n$, which describes the propagation of small amplitude and long waves on the surface of water with viscous effects. Concerning the linearized Cauchy…
We consider the Cauchy problem for systems of semilinear wave equations in two space dimensions. We present a structural condition on the nonlinearity under which the energy decreases to zero as time tends to infinity if the Cauchy data are…
We focus on the general theory to the Cauchy problem for one dimensional nonlinear wave equations with small initial data. In the general theory, we aim to obtain the lower bound estimate of the lifespan of classical solution. In this…
This paper is concerned with the inverse scattering problem of time-harmonic elastic waves by an unbounded rigid rough surface. A direct imaging method is developed to reconstruct the unbounded rough surface from the elastic scattered…
The aim of this paper is first to review the derivation of a model describing the propagation of an optical wave in a photorefractive medium and to present various mathematical results on this model: Cauchy problem, solitary waves.
We consider an inverse problem arising in nonlinear ultrasound imaging. The propagation of ultrasound waves is modeled by a quasilinear wave equation. We make measurements at the boundary of the medium encoded in the Dirichlet-to-Neumann…
We construct a sequence that converges to a solution of the Cauchy problem for a singularly perturbed linear inhomogeneous differential equation of an arbitrary order. This sequence is also an asymptotic sequence in the following sense: the…