TY - JOUR
T1 - A Modified Kernel Method for Solving Cauchy Problem of Two-Dimensional Heat Conduction Equation
AU - Zhao , Jingjun
AU - Liu , Songshu
AU - Liu , Tao
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 31
EP - 42
PY - 2018
DA - 2018/03
SN - 7
DO - http://doi.org/10.4208/aamm.12-m12113
UR - https://global-sci.org/intro/article_detail/aamm/10942.html
KW - 
AB - <p style="text-align: justify;">In this paper, a Cauchy problem of two-dimensional heat conduction
equation is investigated. This is a severely ill-posed problem.
Based on the solution of Cauchy problem of two-dimensional heat
conduction equation, we propose to solve this problem by modifying
the kernel, which generates a well-posed problem. Error estimates
between the exact solution and the regularized solution are given.
We provide a numerical experiment to illustrate the main results.</p>