Singular limit of viscous Cahn-Hilliard equations with memory and dynamic boundary conditions
Ciprian G. Gal, Maurizio Grasselli · Discrete and Continuous Dynamical Systems - B · 2013
We consider a modified Cahn-Hiliard equationwhere the velocity of the order parameter $u$ depends on the pasthistory of $\Delta\mu $, $\mu $ being the chemical potential with an additional viscous term $\alpha u_{t},$ $\alpha >0.$ In addition, the usual no-fluxboundary condition for $u$ is replaced by a nonlinear dynamicboundary condition which accounts for possible interactions withthe boundary. The aim of this work is to analyze the passage tothe singular limit when the memory kernel collapses into a Diracmass. In particular, we discuss the convergence of solutions onfinite time-intervals and we also establish stability results forglobal and exponential attractors.