Location and density determination for a source with impulse derivative time variation

Abstract

In this study an inverse source problem related to the source density f<inf>0</inf>(x) which is a function of bounded support and taking place in the wave equation ?u(x, t) - (1/c2) ?2 u(x, t) / ?t2 = - f<inf>0</inf> (x)??(t) is considered. An explicit expression of the solution is given in terms of the surface integral of the data which is measured on the boundary S of a convex domain D during certain finite time interval [0, T]. An illustrative example shows the applicability as well as the effectiveness of the method. © 2011 IEEE. © 2011 Elsevier B.V., All rights reserved.