Abstract

This paper discusses the inverse problem of determining a spacewise dependent heat source in one-dimensional heat equation in a half infinite domain where data is given at some fixed time. The problem is ill-posed, i.e., the solution, if existing, does not depend continuously on the data. Two regularization solutions of the inverse problem will be given by a simplified Tikhonov regularization method and a modified regularization method. For two regularization solutions, the Hölder type error estimates between the regularization solutions and the exact solution are obtained, respectively. Numerical examples show that two regularization methods are effective for identifying the heat source.