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

证明退化四阶抛物方程ut+Δ(Δup-2Δu)+λup-2u=0,x∈Ω,t>0,p>2在假定具有自然边界条件u=Δu=0,x∈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.

In this paper, we consider a fourth order degenerate parabolic equation δu/δt ＋ △（｜△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 ∈ δΩ,t 〉 0, and the initial condition u（x,0） = u0（x）,x∈Ω, we have proved the existence of uniqueness of weak solution.