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Inverse Estimates for Nonhomogeneous Backward Heat Problems

Author

Listed:
  • Tao Min
  • Weimin Fu
  • Qiang Huang

Abstract

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.

Suggested Citation

  • Tao Min & Weimin Fu & Qiang Huang, 2014. "Inverse Estimates for Nonhomogeneous Backward Heat Problems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:529618
    DOI: 10.1155/2014/529618
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    References listed on IDEAS

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    1. V. A. Morozov, 1984. "Methods for Solving Incorrectly Posed Problems," Springer Books, Springer, number 978-1-4612-5280-1, March.
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