GLOBAL WELL-POSEDNESS FOR A CAHN-HILLIARD EQUATION ON BOUNDED DOMAINS WITH PERMEABLE AND NON-PERMEABLE WALLS IN MAXIMAL REGULARITY SPACES

摘要

We consider the strong solution of the Cahn-Hilliard equation on bounded domains with permeable and non-permeable walls in maximal Lp regularity spaces. From the maximal Lp regularity result of the linear equation with the dynamic boundary condition, the fixed point theorem and a priori estimate, we prove that the solution exists uniquely and globally in time.