Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 04, pp. 1-10.

Title: Regularization and error estimates for nonhomogeneous 
       backward heat problems
       
Authors: Duc Trong Dang (Hochiminh City National Univ., Vietnam)
         Huy Tuan Nguyen (Hochiminh City National Univ., Vietnam)

Abstract: 
 In this article, we study the inverse time problem for the
 non-homogeneous heat equation which is a severely ill-posed problem.
 We regularize this problem using the quasi-reversibility method
 and then obtain error estimates on the approximate solutions.
 Solutions are calculated by the contraction principle
 and shown in numerical experiments. We obtain also rates of
 convergence to the exact solution.
 
Submitted November 11, 2005. Published January 11, 2006.
Math Subject Classifications: 35K05, 35K99, 47J06, 47H10.
Key Words: Backward heat  problem; ill-posed problem;
      contraction principle; quasi-reversibility methods.