# Rate of convergence in the large diffusion limit for the heat equation with a dynamical boundary condition

## TL;DR

This paper investigates how solutions to the heat equation with a dynamical boundary condition converge to Laplace equation solutions as the diffusion coefficient increases, providing insights into the convergence rate.

## Contribution

It establishes the rate of convergence for the heat equation with dynamical boundary conditions in the large diffusion limit.

## Key findings

- Convergence rate to Laplace solutions is quantified.
- Results apply to half-space and exterior domain geometries.
- Provides theoretical foundation for large diffusion asymptotics.

## Abstract

We study the heat equation on a half-space or on an exterior domain with a linear dynamical boundary condition. Our main aim is to establish the rate of convergence to solutions of the Laplace equation with the same dynamical boundary condition as the diffusion coefficient tends to infinity.