具浓度相关黏性系数的黏性Cahn-Hilliard方程解的爆破性质

摘要

We studied the blow-up of the solutions to the viscous Cahn-Hilliard equation with concentration dependent viscosity.The results show that the structural conditons satisfied by the coefficient of viscosity play an important role in the properties of the solutions.Under two different structural conditions of the coefficient of viscosity, using the energy method, we proved that the solutions of the initial boundary value problem blow up in finite time or tend to infinity as t→ + ∞.%研究具浓度相关黏性系数的黏性Cahn-Hilliard方程解的爆破性质.利用能量估计方法,在关于黏性系数的两个不同结构性条件下分别证明了初边值问题的解在有限时刻爆破和时间趋于无穷时解趋于无穷两个性质.结果表明,黏性系数所满足的结构性条件对于方程的解有较大影响.