TY - EJOU AU - Liu, Ji-Chuan AU - Wang, Jun-Gang TI - Cauchy Problem for the Heat Equation in a Bounded Domain Without Initial Value T2 - Computer Modeling in Engineering \& Sciences PY - 2014 VL - 97 IS - 5 SN - 1526-1506 AB - 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. KW - Ill-posed problem KW - Quasi-reversibility method KW - Method of lines KW - Finite difference KW - Convergence estimate DO - 10.3970/cmes.2014.097.437