The large diffusion limit for the heat equation with a dynamical boundary condition

Abstract

We study the heat equation on a half-space with a linear dynamical boundary condition. Our main aim is to show that, if the diffusion coefficient tends to infinity, then the solutions converge (in a suitable sense) to solutions of the Laplace equation with the same dynamical boundary condition.

References in corpus (2)

• Nonlinear elliptic problems with dynamical boundary conditions of reactive and reactive-diffusive type
• Local Hadamard well-posedness and blow-up for reaction-diffusion equations with non-linear dynamical boundary conditions