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Cauchy Problem for the Heat Equation in a Bounded Domain Without Initial Value

Ji-Chuan Liu1, Jun-Gang Wang2

Corresponding author. Department of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu 221116, PR China. Email:
Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi, 710129, PR China.

Computer Modeling in Engineering & Sciences 2014, 97(5), 437-462.


We consider the determination of heat flux within a body from the Cauchy data. The aim of this paper is to seek an approach to solve the onedimensional heat equation in a bounded domain without initial value. This problem is severely ill-posed and there are few theoretic results. A quasi-reversibility regularization method is used to obtain a regularized solution and convergence estimates are given. For numerical implementation, we apply a method of lines to solve the regularized problem. From numerical results, we can see that the proposed method is reasonable and feasible.


Cite This Article

Liu, J., Wang, J. (2014). Cauchy Problem for the Heat Equation in a Bounded Domain Without Initial Value. CMES-Computer Modeling in Engineering & Sciences, 97(5), 437–462.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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