Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
841784 | Nonlinear Analysis: Theory, Methods & Applications | 2011 | 11 Pages |
Abstract
We study the Cauchy problem for the nonlinear heat equation {ut−Δu+u1+σ=0,x∈Rn,t>0,u(0,x)=u0(x),x∈Rn, in the sub critical case of σ∈(0,2n). In the present paper we intend to give a more precise estimate for the remainder term in the asymptotic representation known from paper Escobedo and Kavian (1987) [5]u(t,x)=t−1σw0(xt)+o(t−1σ) as t→∞t→∞ uniformly with respect to x∈Rn, where w0(ξ)w0(ξ) is a positive solution of equation −Δw−ξ2⋅∇w+w1+σ=1σw which decays rapidly at infinity: lim|ξ|→±∞|ξ|2σw0(ξ)=0.
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Authors
Nakao Hayashi, Pavel I. Naumkin,