Nonlinear elliptic problems with dynamical boundary conditions of reactive and reactive-diffusive type

Abstract

We investigate classical solutions of nonlinear elliptic equations with two classes of dynamical boundary conditions, of reactive and reactive-diffusive type. In the latter case it is shown that well-posedness is to a large extent independent of the coupling with the elliptic equation. For both types of boundary conditions we consider blow-up, global existence, global attractors and convergence to single equilibria.