Acta mathematica scientia, Series B >
COMPLEXITY OF ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR THE POROUS MEDIUM EQUATION WITH ABSORPTION
Received date: 2010-04-14
Online published: 2010-11-20
Supported by
This work is partially supported by National Natural Science Foundation of China, partially supported by Specialized Research Fund for the Doctoral Program of Higher Education, and partially supported by Graduate Innovation Fund of Jilin University (20101045).
In this paper we analyze the large time behavior of nonnegative solutions of the Cauchy problem of the porous medium equation with
absorption ut-Δum+γup=0, where γ≥0, m>1and p>m+2/N. We will show that if γ=0 and 0<μ<2N/N(m-1)+2, or γ>0 and 1/p-1<μ<2N/N(m-1)+2, then for any nonnegative function φ in a nonnegative countable subset F of the Schwartz space S(RN), there exists an initial-value u0∈C(RN) with limx→∞u0(x)=0 such that φ is an ω-limit point of the rescaled solutions t u/2u(t β, t), where β=2-u(m-1)/4.
Key words： complexity; asymptotic behavior; porous medium equation
YIN Jing-Xue , WANG Liang-Wei , HUANG Rui . COMPLEXITY OF ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR THE POROUS MEDIUM EQUATION WITH ABSORPTION[J]. Acta mathematica scientia, Series B, 2010 , 30(6) : 1865 -1880 . DOI: 10.1016/S0252-9602(10)60179-8
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