International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 13-16, Pages 741-753
doi:10.1155/S0161171204211383
Determination of a nonlinear source term in a diffusion equation with final observations
Gongsheng Li1
, Yichen Ma2
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
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.