International Journal of Mathematics and Mathematical Sciences 
Volume 2005 (2005), Issue 8, Pages 1221-1237
doi:10.1155/IJMMS.2005.1221

Optimal Tikhonov approximation for a sideways parabolic equation

Chu-Li Fu,1 Hong-Fang Li,1 Xiang-Tuan Xiong,1 and Peng Fu2

 1Department of Mathematics, Lanzhou University, Lanzhou 730000, China
2Institute of Network, School of Electronics and Information Engineering, Xi'an Jiaotong University, Xi'an 710049, China
Received 27 April 2004; Revised 31 December 2004

Abstract

We consider an inverse heat conduction problem with convection term which appears in some applied subjects. This problem is ill posed in the sense that the solution (if it exists) does not depend continuously on the data. A generalized Tikhonov regularization method for this problem is given, which realizes the best possible accuracy.