Identifying Initial Condition in Degenerate Parabolic Equation with Singular Potential

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

International Journal of Differential Equations, 2017, vol. 2017, 1-17

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.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:1467049

DOI: 10.1155/2017/1467049

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