Acta mathematica scientia,Series A ›› 2009, Vol. 29 ›› Issue (6): 1665-1678.

• Articles • Previous Articles     Next Articles

Uniform Blow-up Properties for a Degenerate Parabolic System with Nonlocal Sources

  

  1. Department of Mathematics, Nanjing Xiaozhuang College, Nanjing 210017
  • Received:2007-12-05 Revised:2008-10-16 Online:2009-12-25 Published:2009-12-25
  • Supported by:

    国家自然科学基金(10701024)和江苏省高校自然科学基金(09KJD110008)资助

Abstract:

This paper deals with the blow-up properties of positive solutions to degenerate parabolic systems with nonlocal sources, subject to null Dirichlet boundary conditions. Under appropriate hypotheses, the authors establish the local existence of the solution and the finite time blow-up. Moreover, they obtain a necessary condition for which the two components of the solution blow up simultaneously, and then establish the uniform blow-up profiles in the interior.

Key words: Degenerate parabolic systems, Nonlocal sources, Uniform blow-up profiles,  Simultaneous blow-up

CLC Number: 

  • 35K15
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