Sup-norm estimates for parabolic systems with dynamic boundary conditions

Abstract

We consider parabolic systems with nonlinear dynamic boundary conditions, for which we give a rigorous derivation. Then, we give them several physical interpretations which includes an interpretation for the porousmedium equation, and for certain reaction-diffusion systems that occur in mathematical biology and ecology. We devise several strategies which imply (uniform) L p and L ∞ estimates on the solutions for the initial value problems considered.