On the Semistability of the Minimal Positive Steady State for a Nonhomogeneous Semilinear Cauchy Problem
نویسندگان
چکیده
This paper is contributed to the study of the Cauchy problem <: ut = ∆u+K(|x|)up + μf(|x|) in Rn × (0, T ), u(x, 0) = φ(x) in Rn, u(x, 0) = φ(x) in Rn, with non-negative initial function φ 6≡ 0. We will study the asymptotic behavior and the semistability of the minimal positive steady state. In addition, we will prove that all slow decay positive steady states are stable and weakly asymptotically stable in some weighted L∞ norms.
منابع مشابه
Stability of a Semilinear Cauchy Problem
This paper is contributed to the Cauchy problem ∂u ∂t = ∆u+K(|x|)u p in R × (0, T ), u(x, 0) = φ(x) in R, (0.1) with initial function φ 6≡ 0. The stability and instability of the positive radical steady states, which are positive solutions of ∆u+K(|x|)u = 0, (0.2) has been discussed with different assumption on K(x) and φ under the norm ∗Research supported in part by the Natural Science...
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