Acta mathematica scientia,Series B ›› 2016, Vol. 36 ›› Issue (3): 872-880.doi: 10.1016/S0252-9602(16)30046-7

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OPTIMAL CONDITIONS OF GLOBAL EXISTENCE AND BLOW-UP FOR A NONLINEAR PARABOLIC EQUATION

Yi JIANG, Chuan LUO   

  1. VC/VR Lab and Department of Mathematics, Sichuan Normal University, Chengdu 610066, China
  • Received:2015-02-06 Revised:2015-11-22 Online:2016-06-25 Published:2016-06-25
  • Supported by:

    The first author was supported by National Natural Science Foundation of China (11126336 and 11201324), New Teachers' Fund for Doctor Stations, Ministry of Education (20115134120001), Fok Ying Tuny Education Foundation (141114), Youth Fund of Sichuan Province (2013JQ0027)

Abstract:

According to the variational analysis and the potential well argument, we get the optimal conditions of global existence and blow-up for a type of nonlinear parabolic equations. Furthermore, we give its application in the instability of the steady states.

Key words: nonlinear parabolic equation, variational analysis, potential well argument, global existence, blow up

CLC Number: 

  • 35A15
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