TY - JOUR
T1 - Semi-discretization Difference Approximation for a Cauchy Problem of Heat Equation in Two-dimensional Space
AU - Xiong , Xiangtuan
AU - Li , Jinmei
JO - Journal of Partial Differential Equations
VL - 4
SP - 315
EP - 331
PY - 2015
DA - 2015/12
SN - 28
DO - http://doi.org/10.4208/jpde.v28.n4.3
UR - https://global-sci.org/intro/article_detail/jpde/5119.html
KW - 2D inverse heat conduction problem
KW - Ill-posedness
KW - regularization
KW - error estimate
KW - finite difference
AB -  In this paper we consider a semi-descretization difference scheme for solving a Cauchy problem of heat equation in two-dimensional setting. Some error estimates are proved for the semi-descretization difference regularization method which cannot be fitted into the framework of regularization theory presented by Engl, Hanke and Neubauer. Numerical results show that the proposed method works well.