Abstract

In this paper we study a final value problem for the nonlinear parabolic equation where A is a non negative self-adjoint operator and h is a lipchitz function. Using the stabilized quasi-reversibility method presented by Miller we find optimal perturbations of the operator A, depending on a small parameter to set up non local problem. We show with that the approximate problems are well posed under certain conditions and their solution converges F and all of the original problem has a classical solution. We also obtain estimates for these solutions of the approximate problems and show a convergence result. This paper extends the work by Hettrick and Hughes to non linear ill posed problem