Properties of blow-up solutions to a parabolic system with nonlinear localized terms

Huiling Li; Mingxin Wang

doi:10.3934/dcds.2005.13.683

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2005, Volume 13, Issue 3: 683-700. Doi: 10.3934/dcds.2005.13.683

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Properties of blow-up solutions to a parabolic system with nonlinear localized terms

Huiling Li¹ and
Mingxin Wang^2,

1.
Department of Mathematics, Southeast University, Nanjing 210018
2.
Department of Mathematics, Xuzhou Normal University, Xuzhou 221116, Department of Mathematics, Southeast University, Nanjing 210018

Received: September 2004

Revised: February 2005

Published: April 2005

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Abstract

This paper deals with blow-up properties of the solution to a semi-linear parabolic system with nonlinear localized sources involved in a product with local terms, subject to the null Dirichlet boundary condition. We investigate the influence of localized sources and local terms on blow-up properties for this system. It will be proved that: (i) when $m, q\leq 1$ this system possesses uniform blow-up profiles. In other words, the localized terms play a leading role in the blow-up profile for this case. (ii) when $m, q>1$, this system presents single point blow-up patterns, or say that, in this time, local terms dominate localized terms in the blow-up profile. Moreover, the blow-up rate estimates in time and space are obtained, respectively.

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Mathematics Subject Classification: Primary: 35K15, 35K65.

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