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.
Citation
K. Atifi. Y. Balouki. El-H. Essoufi. B. Khouiti. "Identifying Initial Condition in Degenerate Parabolic Equation with Singular Potential." Int. J. Differ. Equ. 2017 1 - 17, 2017. https://doi.org/10.1155/2017/1467049