Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (3): 1001-1010.doi: 10.1016/S0252-9602(11)60292-0

• Articles • Previous Articles     Next Articles

GLOBAL EXISTENCE AND BLOW-UP OF SOLUTIONS TO A NONLOCAL EVOLUTION p-LAPLACE SYSTEM WITH NONLINEAR BOUNDARY CONDITIONS

 WU Xue-Song1,2, GAO Wen-Jie2*, CAO Jian-Wen1   

  1. 1. Institute of Software, Chinese Academy of Sciences, Beijing 100190, China;
    2. Institute of Mathematics, Jilin University, Changchun 130012, China
  • Received:2009-03-25 Online:2011-05-20 Published:2011-05-20
  • Contact: GAO Wen-Jie E-mail:xswu1978@gmail.com; wjgao@jlu.edu.cn; caojianwen@gmail.com
  • Supported by:

    The project is supported by a grant from the National High Technology Research and Development Program of China (863 Program) (2009AA044501) by NSFC (10776035;  10771085), by Key Lab of Symbolic Computation and Knowledge Engineering of Ministry of Education and by the 985 program of Jilin University.

Abstract:

In this paper, the authors discuss the global existence and blow-up of the solution to an evolution p-Laplace system with nonlinear sources and nonlinear boundary condition. The authors first establish the local existence of solutions, then give a necessary and sufficient condition on the global existence of the positive solution.

Key words: evolution p-Laplacian, nonlinear boundary value problem, nonlinear sources, global existence, blow-up

CLC Number: 

  • 35K55
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