American Institute of Mathematical Sciences

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

 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.
Citation: Huiling Li, Mingxin Wang. Properties of blow-up solutions to a parabolic system with nonlinear localized terms. Discrete & Continuous Dynamical Systems - A, 2005, 13 (3) : 683-700. doi: 10.3934/dcds.2005.13.683
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