@Article{cmes.2014.097.437,
AUTHOR = {Ji-Chuan  Liu, Jun-Gang  Wang},
TITLE = {Cauchy Problem for the Heat Equation in a Bounded Domain Without Initial Value},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {97},
YEAR = {2014},
NUMBER = {5},
PAGES = {437--462},
URL = {http://www.techscience.com/CMES/v97n5/27142},
ISSN = {1526-1506},
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.},
DOI = {10.3970/cmes.2014.097.437}
}