Abstract
In this paper, we investigate the complicated asymptotic behavior of the solutions to the Cauchy problem of a porous medium equation with nonlinear sources when the initial value belongs to a weighted space. AMS Subject Classification:35K55, 35B40.
Highlights
1 Introduction In this paper, we consider the asymptotic behavior of solutions for the Cauchy problem of the porous medium equation with nonlinear sources um = up, in RN × (, ∞), ( . )
In our previous papers [ ], for any bounded sequence {φn}∞ n= in C +(RN ) ≡ {φ ∈ C (RN ); φ(x) ≥ }, we have shown that there exists an initial value u ∈ C (RN ) and a sequence tnk → ∞ as k → ∞ such that μ lim k→∞
We investigate the complicated asymptotic behavior of solutions
Summary
[ – ], while positive global solutions do exist if p > pc ) with the initial value u = ηφ are global and the following estimate holds: u(t) ), in , Vázquez and Zuazua [ ] found that for any bounded sequence {φn}∞ n= in L∞(RN ), there exists an initial value u ∈ Cησ(,M+ ), there exists a sequence tn as n → ∞ satisfying σ tnσ (m– )+
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