Related papers: Introduction to inverse problems for hyperbolic PD…
Multi-wave inverse problems are indirect imaging methods using the interaction of two different imaging modalities. One brings spatial accuracy, and the other contrast sensitivity. The inversion method typically involve two steps. The first…
In this article, we consider linear hyperbolic Initial and Boundary Value Problems (IBVP) in a rectangle (or possibly curvilinear polygonal domains) in both the constant and variable coefficients cases. We use semigroup method instead of…
In the theory and practice of inverse problems for partial differential equations (PDEs) much attention is paid to the problem of the identification of coefficients from some additional information. This work deals with the problem of…
Although there is a substantial body of literature on control and optimization problems for parabolic and hyperbolic systems, the specific problem of controlling and optimizing the coefficients of the associated operators within such…
Under consideration are mathematical models of heat and mass transfer. We study inverse problems of recovering lower-order coefficients in a second order parabolic equation. The coefficients are representable in the form of a finite…
In this paper, a boundary integral method is used to solve an inverse linear heat conduction problem in two-dimensional bounded domain. An inverse problem of measuring the heat flux from partial (on part of the boundary) dynamic boundary…
In this paper we develop a systematic reduction procedure for determining intermediate integrals of second order hyperbolic equations so that exact solutions of the second order PDEs under interest can be obtained by solving first order…
In this article we are concerned with an inverse initial boundary value problem for a non-linear wave equation in space dimension $n\geq 2$. In particular we consider the so called interior determination problem. This non-linear wave…
In this paper, we propose novel proper orthogonal decomposition (POD)--based model reduction methods that effectively address the issue of inverse crime in solving parabolic inverse problems. Both the inverse initial value problems and…
We introduce a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$ - $\Omega$ a…
This review examines classical and recent results on controllability and inverse problems for hyperbolic and dispersive equations with dynamic boundary conditions. We aim to illustrate the applicability of Carleman estimates to establish…
We survey some of our recent results on inverse problems for evolution equations. The goal is to provide a unified approach to solve various types of evolution equations. The inverse problems we consider consist in determining unknown…
We introduced in [arXiv:1106.3204] a method to locate discontinuities of a wave speed in dimension two from acoustic boundary measuments modelled by the hyperbolic Neumann-to-Dirichlet operator. Here we extend the method for sound hard…
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 two inverse problems on a globally hyperbolic Lorentzian manifold $(M,g)$. The problems are: 1. Passive observations in spacetime: Consider observations in a neighborhood $V\subset M$ of a time-like geodesic $\mu$. Under natural…
The BC-method is an approach to inverse problems based on their relations to the boundary control theory. The paper provides a simple and physically transparent description of the method in the case of dynamical inverse data given at a…
We show that a complete Riemannian manifold, as well as time independent smooth lower order terms appearing in a first order symmetric perturbation of a Riemannian wave operator can be uniquely recovered, up to the natural obstructions,…
In this paper we give a more geometrical formulation of the main theorem in [E1] on the inverse problem for the second order hyperbolic equation of general form with coefficients independent of the time variable. We apply this theorem to…
Invariants of general linear system of two hyperbolic partial differential equations (PDEs) are derived under transformations of the dependent and independent variables by real infinitesimal method earlier. Here a subclass of the general…
We demonstrate an application of the spectral method as a numerical approximation for solving Hyperbolic PDEs. In this method a finite basis is used for approximating the solutions. In particular, we demonstrate a set of such solutions for…