Ji-Chuan Liu1, Jun-Gang Wang2
CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.5, pp. 437-462, 2014, DOI:10.3970/cmes.2014.097.437
Abstract 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. More >
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