Special Session 19: 

Asymptotic limits from the viscous Cahn--Hilliard equation to the Cahn--Hilliard and the Allen--Cahn equations on the time-periodic problem

Keiichiro Kagawa
Waseda Univ.
Japan
Co-Author(s):    Mitsuharu \^Otani
Abstract:
We consider the asymptotic limit of the time-periodic problem of the viscous Cahn--Hilliard equation with the Dirichlet boundary condition. We already reported about the existence of the time-periodic solution and the asymptotic limits of the initial value problem for the viscous Cahn--Hilliard equation with the main condition that the nonlinear term is decomposed into a monotone term and a perturbation term. In this talk, we show that the time-periodic solution of the viscous Cahn--Hilliard equation goes to those of the Cahn--Hilliard and the Allen--Cahn equations with some additional conditions.