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2005, Volume 13, Issue 3: 683-700. Doi: 10.3934/dcds.2005.13.683
This issue Previous Article Wellposedness for a parabolic-elliptic system Next Article Attractors for nonautonomous 2d Navier-Stokes equations with normal external forces

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

  • 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
Abstract Related Papers Cited by
    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.
    Mathematics Subject Classification: Primary: 35K15, 35K65.

    Citation:
    shu

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