Total versus single point blow-up in heat equations with coupled localized sources

Article type: Research Article

Authors: Zheng, Sining | Wang, Jinhuan

Affiliations: Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, P.R. China E-mail: snzheng@dlut.edu.cn

Note: [] Corresponding author.

Abstract: This paper considers heat equations with local and coupled localized sources subject to null Dirichlet boundary conditions. The behavior of solutions depends on the interactions among the local and localized sources as well as the diffusions with the null boundary conditions in the model. The aim of the paper is to distinguish total and single point blow-up for the non-global solutions. In addition, simultaneous versus non-simultaneous blow-up of solutions under different dominations are determined also with four possible simultaneous blow-up rates.

Keywords: nonlinear localized sources, total blow-up, single point blow-up, blow-up rate, characteristic algebraic system, simultaneous blow-up, non-simultaneous blow-up

Journal: Asymptotic Analysis, vol. 51, no. 2, pp. 133-156, 2007