Critical slowing down for relaxation in the Cahn–Hilliard equation with dynamic boundary conditions

抄録

In this paper, we report the behavior of solutions of the one-dimensional Cahn–Hilliard equation with dynamic boundary conditions, where the time evolution on the boundary is induced by the boundary derivative. By studying the time evolution from a certain initial value, we find that as the time constant on the boundary asymptotically approaches a certain value, the relaxation to a stable stationary solution slows down at a logarithmic rate. This phenomenon is not observed in the case of the Neumann boundary condition.