On an inverse source problem connected with photo-acoustic and thermo-acoustic tomographies

Abstract

An inverse source problem which aims to determine the source density p(0)(x) taking place in the wave equation Delta p(x, t) - (1/c(2))partial derivative(2)p(x, t)/partial derivative t(2) = -p(0)(x)delta'(t) is considered. One assumes that p(0)(x) is a function of bounded support while p(0)(x, t) can be measured on the boundary S of a convex domain D during a certain finite time interval [0,T]. An explicit expression of the solution is given in terms of the surface integral of the data on S. Two illustrative examples show the applicability as well as the effectiveness of the method. In one of these examples S consists of a spheroid while in the other it consists of a half of the spheroid and a disc. The problem is motivated by photo-acoustic and thermo-acoustic applications. (C) 2012 Elsevier B.V. All rights reserved.