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April  2005, 13(3): 683-700. doi: 10.3934/dcds.2005.13.683

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

Huiling Li 1, and  Mingxin Wang 2,

1. 

Department of Mathematics, Southeast University, Nanjing 210018, China
2. 

Department of Mathematics, Xuzhou Normal University, Xuzhou 221116, Department of Mathematics, Southeast University, Nanjing 210018, China

Received  September 2004 Revised  February 2005 Published  May 2005

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.
Keywords: blow-up rate estimate., uniform blow-up profile, nonlinear local terms, single point blow-up pattern, nonlinear localized sources, Parabolic system.
Mathematics Subject Classification: Primary: 35K15, 35K6.
Citation: Huiling Li, Mingxin Wang. Properties of blow-up solutions to a parabolic system with nonlinear localized terms. Discrete and Continuous Dynamical Systems, 2005, 13 (3) : 683-700. doi: 10.3934/dcds.2005.13.683
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