Acta mathematica scientia,Series B ›› 2013, Vol. 33 ›› Issue (4): 1024-1030.doi: 10.1016/S0252-9602(13)60060-0

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BLOW-UP OF THE SOLUTION FOR A CLASS OF POROUS MEDIUM EQUATION WITH POSITIVE INITIAL ENERGY

 WU Xiu-Lan1,2, GAO Wen-Jie1*   

  1. 1. Institute of Mathematics, Jilin University, Changchun 130012, China
    2. College of Mathematics, Jilin Normal University, Siping 136000, China
  • Received:2012-05-14 Online:2013-07-20 Published:2013-07-20
  • Contact: GAO Wen-Jie,wjgao@jlu.edu.cn E-mail:chjlsywxl@126.com; wjgao@jlu.edu.cn
  • Supported by:

    The project is supported by NSFC (11271154), Key Lab of Symbolic Computation and Knowledge Engineering of Ministry of Education and by the 985 Program of Jilin University.

Abstract:

This paper deals with a class of porous medium equation
ut = Δum + f(u)
with homogeneous Dirichlet boundary conditions. The blow-up criteria is established by using the method of energy under the suitable condition on the function f(u).

Key words: porous medium equation, blow-up, positive initial energy

CLC Number: 

  • 35K55
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