Two new regularization methods for solving sideways heat equation

Journal of inequalities and applications

Huy Tuan Nguyen¹ 

关键词: Cauchy problem;    sideways heat equation;    ill-posed problem;    error estimates;    35K05;    35K99;    47J06;    47H10;   

DOI  :  10.1186/s13660-015-0564-0

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We consider a non-standard inverse heat conduction problem in a bounded domain which appears in some applied subjects. We want to know the surface temperature in a body from a measured temperature history at a fixed location inside the body. This is an exponentially ill-posed problem in the sense that the solution (if it exists) does not depend continuously on the data. In this paper, we introduce the two new classes of quasi-type methods and iteration methods to solve the problem and prove that our methods are stable under both a priori and a posteriori parameter choice rules. An appropriate selection of a parameter in the scheme will get a satisfactory approximate solution. Furthermore, if we use the discrepancy principle we can avoid the selection of the a priori bound.

【 授权许可】

CC BY