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

TL;DR

This paper studies nonlinear elliptic equations with reactive and reactive-diffusive dynamical boundary conditions, analyzing well-posedness, blow-up, global existence, attractors, and convergence to equilibria.

Contribution

It provides new insights into the well-posedness and long-term behavior of solutions under these complex boundary conditions.

Findings

Well-posedness largely independent of coupling in reactive-diffusive case

Conditions for blow-up and global existence established

Existence of global attractors and convergence results

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.