Identification of a discontinuous source in the heat equation

Abstract

In this paper the feasibility of identification of a discontinuous source term in a parabolic equation is investigated. It is shown that a minimal set of data according to uniqueness of the inverse problem is given by flux measurements in time at two distinct points on the boundary. Besides the uniqueness result iterative regularization schemes are developed. The methods are based on the domain derivative and a general existence theory and a representation of the domain derivative for parabolic equations is derived.