Abstract
The extinction phenomenon of solutions for the homogeneous Dirichlet boundary value problem of the porous medium equation , is studied. Sufficient conditions about the extinction and decay estimates of solutions are obtained by using -integral model estimate methods and two crucial lemmas on differential inequality.
Highlights
Introduction and main resultsThis paper is devoted to the extinction and decay estimates for the porous medium equation ut = Δum + λ|u|p−1u − βu, x ∈ Ω, t > 0, u(x, t) = 0, x ∈ ∂Ω, t > 0, (1.1) (1.2)u(x, 0) = u0(x) ≥ 0, x ∈ Ω, (1.3)with 0 < m < 1 and p,λ,β > 0, where Ω ⊂ RN (N > 2) is a bounded domain with smooth boundary.The phenomenon of extinction is an important property of solutions for many evolutionary equations which have been studied extensively by many researchers
There are some papers concerning the extinction for the porous medium equation
As far as we know, few works are concerned with the decay estimates of solutions for the porous medium equation
Summary
The extinction phenomenon of solutions for the homogeneous Dirichlet boundary value problem of the porous medium equation ut = Δum + λ|u|p−1u − βu, 0 < m < 1, is studied. Sufficient conditions about the extinction and decay estimates of solutions are obtained by using Lp-integral model estimate methods and two crucial lemmas on differential inequality. This paper is devoted to the extinction and decay estimates for the porous medium equation ut = Δum + λ|u|p−1u − βu, x ∈ Ω, t > 0, u(x, t) = 0, x ∈ ∂Ω, t > 0, (1.1) (1.2)
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