Inverse Estimates for Nonhomogeneous Backward Heat Problems | Zendy

Min Tao | Zendy; Weimin Fu | Zendy; Qiang Huang | Zendy

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Inverse Estimates for Nonhomogeneous Backward Heat Problems

Author(s) -

Min Tao,

Weimin Fu,

Qiang Huang

Publication year - 2014

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2014/529618

Subject(s) - tikhonov regularization , fredholm integral equation , regularization (linguistics) , inverse problem , mathematics , computation , heat equation , well posed problem , backus–gilbert method , inverse , integral equation , inversion (geology) , mathematical optimization , mathematical analysis , regularization perspectives on support vector machines , algorithm , computer science , geometry , paleontology , structural basin , artificial intelligence , biology

We investigate the inverse problem in the nonhomogeneous heat equation involving the recovery of the initial temperature from measurements of the final temperature. This problem is known as the backward heat problem and is severely ill-posed. We show that this problem can be converted into the first Fredholm integral equation, and an algorithm of inversion is given using Tikhonov's regularization method. The genetic algorithm for obtaining the regularization parameter is presented. We also present numerical computations that verify the accuracy of our approximation

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