SINGULAR LIMIT OF VISCOUS CAHN-HILLIARD EQUATIONS WITH MEMORY AND DYNAMIC BOUNDARY CONDITIONS

摘要

We consider a modified Cahn-Hiliard equation where the velocity of the order parameter u depends on the past history of △μ, μ being the chemical potential with an additional viscous term αu_t, α > 0. In addition, the usual no-flux boundary condition for u is replaced by a nonlinear dynamic boundary condition which accounts for possible interactions with the boundary. The aim of this work is to analyze the passage to the singular limit when the memory kernel collapses into a Dirac mass. In particular, we discuss the convergence of solutions on finite time-intervals and we also establish stability results for global and exponential attractors.