Fatma KANCA, İrem BAGLAN

Identifying an unknown time dependent coefficient for quasilinear parabolic equations

ISSN: 2147-5520
Başlangıç: 2015
Yayıncı: Biska Bilişim

This article deals with the mathematical analysis of the inverse problem of identifying the unknown time-dependent coefficient in the quasilinear parabolic equation with the nonlocal boundary and integral overdetermination conditions. The existence, uniqueness and continuously dependence upon the data of the solution are proved by iteration method in addition to the numerical solution of this problem is considered with an example.

Keywords:

Quasilinear parabolic equation, inverse problem nonlocal boundary condition, finite difference method,

PDF

___

Kanca F.,Baglan I., Continuous dependence on data for a solution of the quasilinear parabolic equation with a periodic boundary condition, Boundary Value Problems, 28, 2013.
Sakınc I., Numerical Solution of a Quasilinear Parabolic Problem with Periodic Boundary Condition, Hacettepe Journal of Mathematics and Statistics, 2010;39(2):183-189.
A. M. Nakhushev, Equations of Mathematical Biology, Moscow, 1995 (in Russian).
Ionkin NI. Solution of a boundary-value problem in heat conduction with a nonclassical boundary condition. Differential Equations.1977; 13: 204-211
Pourgholia R, Rostamiana M and Emamjome M., A numerical method for solving a nonlinear inverse parabolic problem. Inverse Problems in Science and Engineering, 2010, 18(8):1151-1164.
Cannon J,R., Lin Y., Determination of parameter p(t) in Hölder classes for some semilinear parabolic equations. Inverse Problems, 1988, 4:595-606.
Ozbilge E., Demir A., Inverse problem for a time-fractional parabolic equation, Journal of Inequalities and Applications, 2015, 81, (Mar 2015).