Frontiers of Mathematics in China >

2010 , Vol. 5 >Issue 2: 341 - 359

DOI: https://doi.org/10.1007/s11464-010-0007-7

Research articles

Total versus single point blow-up in a localized heat system

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  • 1.Department of Mathematics, Liaoning University, Shenyang 110036, China；School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China; 2.School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China;

Published date: 05 Jun 2010

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Abstract

This paper considers a heat system with localized sources and local couplings subject to null Dirichlet boundary conditions, for which both total and single point blow-up are possible. The aim of the paper is to identify the total and single point blow-up via a complete classification for all the nonlinear parameters in the model. As preliminaries of the paper, simultaneous versus non-simultaneous blow-up of solutions is involved, too. The results are then compared with those for another kind of heat system coupled via localized sources in a previous paper of the authors.

Key words： Localized source; total blow-up; single point blow-up; blow-up set; simultaneous blow-up; non-simultaneous blow-up

Cite this article

Jinhuan WANG, Sining ZHENG, . Total versus single point blow-up in a localized heat system[J]. Frontiers of Mathematics in China, 2010 , 5(2) : 341 -359 . DOI: 10.1007/s11464-010-0007-7

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