Backward heat equations with locally lipschitz source

Abstract

Let be in and let , be a locally Lipschitz function with respect to the variable and . In this article, we consider the following backward heat problem with a nonlinear heat source The problem is ill-posed in the sense of Hadamard. Hence a regularization is in order. We use the -dimensional Fourier transform to construct an approximate solution for this problem. We also prove error estimates for our problem and give comments on similar problems.