On a backward nonlinear parabolic equation with time and space dependent thermal conductivity: Regularization and error estimates

Abstract

Abstract. We study the inverse problem for nonlinear parabolic equation with variable thermal conductivity a ( x , t ) ${a(x,t)}$ which is a ill-posed problem. We regularize this problem by using the truncated integral method and then obtain the error estimate between the exact solution and the regularized solution. A numerical experiment is given for illustrating our method.