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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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

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

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

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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.

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