International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 14, Pages 741-753
Determination of a nonlinear source term in a diffusion equation
with final observations
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 Gongsheng Li 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.
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.