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

Abstract:
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.

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

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