一类带梯度依赖势和源的粘性Cahn-Hilliard方程解的爆破现象

Blow-Up Phenomena of Solutions for a Class of Viscous Cahn-Hilliard Equation with Gradient Dependent Potentials and Sources

该文讨论了一类带梯度依赖势和源的粘性Cahn-Hilliard方程解的爆破现象.使用能量方法,微分不等式和积的导数公式建立了爆破准则和确定了爆破时间的上界;利用微分不等式和积的导数公式确定了爆破时间的下界.

In this manuscript, we study the blow-up phenomena of solutions for a class of viscous Cahn-Hilliard equation with gradient dependent potentials and source. We establish a criterion for blow-up and determine the upper bound for blow-up time by the energy method, the differential inequality and the derivative formula of the product;We determine the lower bounds for blow-up time by the differential inequality and the derivative formula of the product.