具有一般非线性项的Cahn-Hilliard方程的整体吸引子

Global Attactor for Cahn-Hilliard Equations with More General Nonlinear Term

改变了Cahn Hilliard方程 : u t-△k(u) =0 , k(u) =-λ△u+f(u) , u n =- △u n =0 ,u(x ,0 ) =u0 (x)的非线性项f(u) ,用较一般限制条件代替了“f(u)是首项系数为正的奇数多项式”这一条件 ,并证明了该方程存在紧连通整体吸引子 .

In this paper, the existence of compact and connected global attractor for the Cahn Hilliard equationsut-△k(u)=0, k(u)=-λ△u+f(u), un=-△un=0, u(x,0)=u 0(x)is transformed. The condition that f(u) is a polynomial of odd degree with a positive leadin coefficient is replaced by move general limited one. It is proved that such system possesses a compact and connected global attractor.