A modified quasi-boundary value method for regularizing of a backward problem with time-dependent coefficient

Abstract

In this article, we consider a classical ill-posed problem which is the backward problem for parabolic equation with time-dependent coefficient uxx(x, t)= a(t)ut(x, t), (x, t) ε R ×[0, T]. Applying the method of Fourier transform and the modified quasi-boundary value method, we shall give a regularization for the problem. A sharp error estimate between the regularized solution and the exact solution is given in this article. A numerical experiment is provided illustrating the main results. © 2011 Taylor & Francis.