A Ritz-Galerkin approximation to the solution of parabolic equation with moving boundaries

Boundary value problems

Jianrong Zhou¹  Heng Li³ 

[1] Department of Mathematics, Foshan University, Foshan, People’Department of Mathematics, University of Louisville, Louisville, United States;s Republic of China

关键词: Ritz-Galerkin method;    Bernstein polynomial basis;    parabolic equation;    moving boundaries;    initial boundary value problem;    approximation solution;    ductal carcinoma in situ (DCIS) model;    35K05;    35K15;    35K20;    35Q68;   

DOI  :  10.1186/s13661-015-0503-5

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The present paper is devoted to the investigation of a parabolic equation with moving boundaries arising in ductal carcinoma in situ (DCIS) model. Approximation solution of this problem is implemented by Ritz-Galerkin, which is a first attempt at tackling such problem. In process of dealing with this moving boundary condition, we use a trick of introducing two transformations to convert moving boundary to nonclassical boundary that can be handled with Ritz-Galerkin method. Also, existence and uniqueness are proved. Illustrative examples are included to demonstrate the validity and applicability of the technique in this paper.

【 授权许可】

CC BY