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.

31 pages

References in corpus (2)

• Convergence to equilibrium for the semilinear parabolic equation with dynamical boundary condition
• Fredholm alternative, semilinear elliptic problems, and Wentzell boundary conditions

Cited by in corpus (4)

• On second-order and fourth-order elliptic systems consisting of bulk and surface PDEs: Well-posedness, regularity theory and eigenvalue problems
• Solvability of the heat equation on a half-space with a dynamical boundary condition and unbounded initial data
• The large diffusion limit for the heat equation with a dynamical boundary condition
• On a perturbed fast diffusion equation with dynamic boundary conditions