具有惯性项和阻尼项的Cahn-Hilliard方程的整体吸引子

本文研究具有惯性项和阻尼项的亚三次非线性Cahn-Hilliard方程的初边值问题.在非线性弱正则的条件下,我们建立弱解的适定性,而不考虑非线性项的一阶导数的下界条件.接着利用弱解的渐近紧和能量解的严格Lyapunov函数的存在性,证明在空间(H2(Ω)∩H0^1(Ω))×L^2(Ω).上存在整体吸引子.

Global Attractor for the Cahn-Hilliard Equation with Inertial Term and Damping Term

In this paper,we consider the initial boundary value problem of sub-cubic nonlinearity Cahn-Hilliard equation with inertial term and damping term.Under mild regularity conditions on the nonlinearity,we prove the uniform boundedness of the solutions without considering lower bound condition on the first derivative of the nonlinear term.Then,we first establish the asymptoticwe compactness of the weak solutions.Next,taking advantage of the presence of strict Lyapunov function for the energy solutions,we prove the existence of the global attractor in(H2(Ω)∩H0^1(Ω))×L^2(Ω).