Identifying initial condition in degenerate parabolic equation with singular potential
type: Item
instance of: scholarly article
title: Identifying initial condition in degenerate parabolic equation with singular potential
zbMATH Open document ID: 1487.35228
DOI: 10.1155/2017/1467049
author: Y. Balouki
author: B. Khouiti
author: Khalid Atifi
author: El-Hassan Essoufi
published in: International Journal of Differential Equations
publication date: 2018-08-10T00:00:00Z
review text: Summary: A hybrid algorithm and a 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 heat evolution 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.
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35K67
zbMATH DE Number: 6915923
Wikidata QID: Q59144268
describes a project that uses: Genocop
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/1467049
OpenAlex ID: W2625589402
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description: scientific article; zbMATH DE number 6915923