International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 14, Pages 741-753
doi:10.1155/S0161171204211383

Determination of a nonlinear source term in a diffusion equation with final observations

Gongsheng Li,1 Yichen Ma,2 and Kaitai Li2

1School of Mathematics and Information Science, Shandong University of Technology, Shandong, Zibo 255049, China
2School of Sciences, Xi'an Jiaotong University, Shannxi, Xi'an 710049, China

Received 25 November 2002

Copyright © 2004 Hindawi Publishing Corporation. 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

This paper deals with an inverse problem of determining a nonlinear source term in a quasilinear diffusion equation with overposed final observations. Applying integral identity methods, data compatibilities are deduced by which the inverse source problem here is proved to be reasonable and solvable. Furthermore, with the aid of an integral identity that connects the unknown source terms with the known data, a conditional stability is established.