International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 943621, 20 pages
http://dx.doi.org/10.1155/2012/943621
Research Article

A Regularization of the Backward Problem for Nonlinear Parabolic Equation with Time-Dependent Coefficient

Pham Hoang Quan,1 Le Minh Triet,1 and Dang Duc Trong2

1Department of Mathematics and Applications, Sai Gon University, 273 An Duong Vuong, District 5, Ho Chi Minh City, Vietnam
2Department of Mathematics, University of Natural Science, Vietnam National University, 227 Nguyen Van Cu, District 5, Ho Chi Minh City, Vietnam

Received 31 March 2012; Revised 21 June 2012; Accepted 11 August 2012

Academic Editor: Theodore E. Simos

Copyright © 2012 Pham Hoang Quan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the backward problem with time-dependent coefficient which is a severely ill-posed problem. We regularize this problem by combining quasi-boundary value method and quasi-reversibility method and then obtain sharp error estimate between the exact solution and the regularized solution. A numerical experiment is given in order to illustrate our results.