摘要
In this paper we analyze the large time behavior of nonnegative solutions of the Cauchy problem of the porous medium equation with absorption ut - △um + yup = 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→∞ uo(x)= 0 such that φ is an w-limit point of the rescaled solutions tμ/2u(tβ, t), Where β = 2-μ(m-1)/4.
In this paper we analyze the large time behavior of nonnegative solutions of the Cauchy problem of the porous medium equation with absorption ut - △um + yup = 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→∞ uo(x)= 0 such that φ is an w-limit point of the rescaled solutions tμ/2u(tβ, t), Where β = 2-μ(m-1)/4.
基金
supported by National Natural Science Foundation of China
supported by Specialized Research Fund for the Doctoral Program of Higher Education
supported by Graduate Innovation Fund of Jilin University (20101045)