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 |
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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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