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

Jingjun Zhao, Songshu Liu & Tao Liu

DOI: 10.4208/aamm.12-m12113

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

Published online: 2018-03

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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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@Article{AAMM-7-31, author = {Zhao , JingjunLiu , Songshu and Liu , Tao}, title = {A Modified Kernel Method for Solving Cauchy Problem of Two-Dimensional Heat Conduction Equation}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {7}, number = {1}, pages = {31--42}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.12-m12113}, url = {http://global-sci.org/intro/article_detail/aamm/10942.html} }
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 -

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.

Zhao , JingjunLiu , Songshu and Liu , Tao. (2018). A Modified Kernel Method for Solving Cauchy Problem of Two-Dimensional Heat Conduction Equation. Advances in Applied Mathematics and Mechanics. 7 (1). 31-42. doi:10.4208/aamm.12-m12113
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