Acta mathematica scientia,Series B

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THE EXISTENCE OF GLOBAL SOLUTION AND THE BLOWUP PROBLEM FOR SOME p-LAPLACE HEAT EQUATIONS

Wang Yang   

  1. Department of Mathematics, East China Normal University, Shanghai 200062, China
  • Received:2003-12-30 Revised:2005-09-24 Online:2007-04-20 Published:2007-04-20
  • Contact: Wang Yang

Abstract:

This article consider, for the following
heat equation
{ut|x|sΔpu=uq,  (x,t)Ω×(0,T),u(x,t)=0,(x,t)Ω×(0,T),u(x,0)=u0(x),u0(x)0,u0(x)0


the existence of global solution under some conditions and give two sufficient conditions
for the blow up of local solution in finite time, where Ω is a smooth bounded domain
in RN(N>p), $0\in \Omega ,\Delta_p u={\rm div}(|\nabla u|^{p-2}\nabla u),0\le s\le 2,
p\ge 2, p-1

CLC Number: 

  • 35K20
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