Volume 7, Issue 1
A Modified Kernel Method for Solving Cauchy Problem of Two-Dimensional Heat Conduction Equation

Jingjun Zhao, Songshu Liu & Tao Liu

Adv. Appl. Math. Mech., 7 (2015), pp. 31-42.

Published online: 3431-08

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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.

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