一个退化四阶抛物方程弱解的惟一性

The Uniqueness of Weak Solution for a Degenerate Fourth Order Parabolic Equation

关键词:  抛物方程  弱解  惟一性

Key words:  parabolic equation  weak solution  uniqueness

摘要:

证明退化四阶抛物方程∂u/∂t+△(|△u|^p-2△u)+λ|u|^p-2u=O,x∈Ω,t>0,p>2在假定具有自然边界条件u=△u=0,△∈∂Ω,t>0,以及初始值条件u(x,0)=u₀(x),x∈Ω下,存在弱解惟一性.

Abstract:

In this paper, we consider a fourth order degenerate parabolic equation ∂u/∂t + △ (|△u|^p-2△u) +λ|u|^p-2u=0, x∈Ω, t > 0, p > 2. Under some assumptions on the natural boudary conditions u=△u=0, x ∈ ∂Ω, t > 0, and the initial condition u (x, 0)=u₀ (x), x∈Ω, we have proved the existence of uniqueness of weak solution.