COMPUTATIONAL SOLUTION OF BLOW-UP PROBLEMS FOR SEMILINEAR PARABOLIC PDEs ON UNBOUNDED DOMAINS

被引：20

作者：

Brunner, Hermann ^{[1
,2
]}

Wu, Xiaonan ^{[2
]}

Zhang, Jiwei ^{[3
]}

机构：

[1] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada

[2] Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong, Peoples R China

[3] Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 637371, Singapore

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2010年 / 31卷 / 06期

基金：

加拿大自然科学与工程研究理事会;

关键词：

semilinear partial differential equations; unbounded spatial domains; finite-time blow-up; local absorbing boundary conditions; finite difference spatial discretization; adaptive time stepping; BOUNDARY-CONDITIONS; NUMERICAL-METHOD; EQUATION; BEHAVIOR;

D O I：

10.1137/090761367

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the numerical solution of semilinear parabolic PDEs on unbounded spatial domains whose solutions blow up in finite time. The focus of the presentation is on the derivation of the nonlinear absorbing boundary conditions for one-dimensional and two-dimensional computational domains and on a simple but efficient adaptive time-stepping scheme. The theoretical results are illustrated by a broad range of numerical examples, including problems with multiple blow-up points.

引用

页码：4478 / 4496

页数：19

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