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A Modified Kernel Method for Solving Cauchy Problem of Two-Dimensional Heat Conduction Equation

Published online by Cambridge University Press:  09 January 2015

Jingjun Zhao ,
Songshu Liu  and
Tao Liu
Jingjun Zhao*
Affiliation:
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Songshu Liu
Affiliation:
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Tao Liu
Affiliation:
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
*
*Email:hit_zjj@hit.edu.cn(J. J. Zhao)
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Abstract

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.

Keywords

47A5265J22Ill-posed problemCauchy problemmodified kernel method
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 7 , Issue 1 , February 2015 , pp. 31 - 42
Copyright
Copyright © Global Science Press Limited 2015 

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