Electron. J. Diff. Equ., Vol. 2015 (2015), No. 245, pp. 1-10.

An inverse coefficient problem for a nonlinear reaction diffusion equation with a nonlinear source

SalIh Tatar, Suleyman Ulusoy

In this article, we consider the problem of identifying an unknown coefficient in a nonlinear diffusion equation. Under appropriate conditions, we prove the existence and the uniqueness of solution for the inverse problem. For the numerical solution of the inverse problem, a numerical method based on discretization of the minimization problem, steepest descent method and least squares approach is proposed. A numerical example is given to illustrate applicability and high accuracy of the proposed method.

Submitted August 4, 2015. Published September 22, 2015.
Math Subject Classifications: 35R30, 65M32, 65N20.
Key Words: Inverse problem; class of admissible coefficients; maximum principle; steepest descent method; least squares approach.

Show me the PDF file (216 KB), TEX file, and other files for this article.

Salih Tatar
Department of Mathematics
Faculty of Education, Zirve University,
Sahinbey, Gaziantep 27260, Turkey
email: salih.tatar@zirve.edu.tr
Suleyman Ulusoy
Department of Mathematics
Faculty of Education, Zirve University
Sahinbey, Gaziantep 27260, Turkey
email: suleyman.ulusoy@zirve.edu.tr

Return to the EJDE web page