Acta mathematica scientia, Series B >
LARGE TIME BEHAVIOR OF SOLUTIONS TO NEWTONIAN FILTRATION EQUATIONS WITH SOURCES
Received date: 2008-03-31
Online published: 2010-05-20
Supported by
This work is supported by the NNSF of China
This article is concerned with large time behavior of solutions to the Neumann or Dirichlet problem for a class of Newtonian filtration
equations
|x|λ+k ∂u / ∂t =div(|x|k \nabla um)+|x|λ+kup
with 0<m<1, p>1, λ ≥0, k ∈ R. An interesting phenomenon is that there exist two thresholds k∞ and k1 for the exponent k, such that the critical Fujita exponent pc for p exists and is finite if k ∈ (k∞, k1), otherwise, pc is infinite or does not exist.
WANG Lu-Sheng , YIN Jing-Xue , WANG Ze-Jia . LARGE TIME BEHAVIOR OF SOLUTIONS TO NEWTONIAN FILTRATION EQUATIONS WITH SOURCES[J]. Acta mathematica scientia, Series B, 2010 , 30(3) : 968 -974 . DOI: 10.1016/S0252-9602(10)60094-X
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