International Journal of Differential Equations

Identifying Initial Condition in Degenerate Parabolic Equation with Singular Potential

K. Atifi, Y. Balouki, El-H. Essoufi, and B. Khouiti

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Abstract

A hybrid algorithm and regularization method are proposed, for the first time, to solve the one-dimensional degenerate inverse heat conduction problem to estimate the initial temperature distribution from point measurements. The evolution of the heat is given by a degenerate parabolic equation with singular potential. This problem can be formulated in a least-squares framework, an iterative procedure which minimizes the difference between the given measurements and the value at sensor locations of a reconstructed field. The mathematical model leads to a nonconvex minimization problem. To solve it, we prove the existence of at least one solution of problem and we propose two approaches: the first is based on a Tikhonov regularization, while the second approach is based on a hybrid genetic algorithm (married genetic with descent method type gradient). Some numerical experiments are given.

Article information

Source
Int. J. Differ. Equ., Volume 2017 (2017), Article ID 1467049, 17 pages.

Dates
Received: 28 September 2016
Revised: 13 March 2017
Accepted: 19 March 2017
First available in Project Euclid: 19 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1500429718

Digital Object Identifier
doi:10.1155/2017/1467049

Mathematical Reviews number (MathSciNet)
MR3666266

Zentralblatt MATH identifier
06915923

Citation

Atifi, K.; Balouki, Y.; Essoufi, El-H.; Khouiti, B. Identifying Initial Condition in Degenerate Parabolic Equation with Singular Potential. Int. J. Differ. Equ. 2017 (2017), Article ID 1467049, 17 pages. doi:10.1155/2017/1467049. https://projecteuclid.org/euclid.ijde/1500429718


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