Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2014, Special Issue (2013), Article ID 529618, 7 pages.

Inverse Estimates for Nonhomogeneous Backward Heat Problems

Tao Min, Weimin Fu, and Qiang Huang

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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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J. Appl. Math., Volume 2014, Special Issue (2013), Article ID 529618, 7 pages.

First available in Project Euclid: 1 October 2014

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Min, Tao; Fu, Weimin; Huang, Qiang. Inverse Estimates for Nonhomogeneous Backward Heat Problems. J. Appl. Math. 2014, Special Issue (2013), Article ID 529618, 7 pages. doi:10.1155/2014/529618.

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