通过移动媒质避免爆破

数学季刊 ›› 2005, Vol. 20 ›› Issue (2): 167-177.

通过移动媒质避免爆破

Department of Applied Mathematics, Information Engineering University, Zhengzhou 450002, China; College of Mathematics, Shandong University, Jinan 250100, China

收稿日期:2004-06-24 出版日期:2005-06-30 发布日期:2024-01-22
作者简介:YAO Li(1980-),female,native of Kaijiang,Sichuan,a postgraduate of Information Engineering University,engages in differential equations analysis;LIU Yun-xian(1973-),female,native of Penglai,Shandong, an associate professor of Shandong University,Ph.D.,engages in numerical solutions for PDEs;YANG Peng- fei(1978-),male,native of Nanzhao,Henan,an assistant of Information Engineering University,engages in applied mathematics.
基金资助:
Supported by the Innovation Project for University Prominent Research Talents of Henan (2003KJCX008)；

Avoidance of Blow-up by Moving Medium

Department of Applied Mathematics, Information Engineering University, Zhengzhou 450002, China; College of Mathematics, Shandong University, Jinan 250100, China

Received:2004-06-24 Online:2005-06-30 Published:2024-01-22
About author:YAO Li(1980-),female,native of Kaijiang,Sichuan,a postgraduate of Information Engineering University,engages in differential equations analysis;LIU Yun-xian(1973-),female,native of Penglai,Shandong, an associate professor of Shandong University,Ph.D.,engages in numerical solutions for PDEs;YANG Peng- fei(1978-),male,native of Nanzhao,Henan,an assistant of Information Engineering University,engages in applied mathematics.
Supported by:
Supported by the Innovation Project for University Prominent Research Talents of Henan (2003KJCX008)；

摘要/Abstract

摘要： This paper deals with two parabolic initial-boundary value problems in multidimensional domain. The first problem describes the situation where the spherical medium is static and the nonlinear reaction takes place only at a single point. We show that under some conditions, the solution blows up in finite time and the blow-up set is the whole spherical medium. When the spherical medium is allowed to move in a special space, we investigate another parabolic initial-boundary value problem. It is proved that the blow-up can be avoided if the acceleration of the motion satisfies certain conditions.

关键词: moving , medium, blow-up, parabolic , problem

Abstract: This paper deals with two parabolic initial-boundary value problems in multidimensional domain. The first problem describes the situation where the spherical medium is static and the nonlinear reaction takes place only at a single point. We show that under some conditions, the solution blows up in finite time and the blow-up set is the whole spherical medium. When the spherical medium is allowed to move in a special space, we investigate another parabolic initial-boundary value problem. It is proved that the blow-up can be avoided if the acceleration of the motion satisfies certain conditions.

Key words: moving , medium, blow-up, parabolic , problem

中图分类号:

O175.8

姚俐, 刘蕴贤, 杨鹏飞. 通过移动媒质避免爆破[J]. 数学季刊, 2005, 20(2): 167-177.

YAO Li, LIU Yun-xian, YANG Peng-fei. Avoidance of Blow-up by Moving Medium[J]. Chinese Quarterly Journal of Mathematics, 2005, 20(2): 167-177.

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