A Note on Moser Iteration and the Large Coupling Limit

TL;DR

This paper studies the behavior of heat semigroups with large coupling in bounded domains, demonstrating sub-exponential decay in subdomains of the obstacle using Moser iteration techniques.

Contribution

It introduces a novel application of Moser iteration to analyze the large coupling limit in singularly perturbed heat equations.

Findings

Sub-exponential decay in the large coupling limit

Effective analysis of diffusion in obstacle models

Application of Moser iteration to singular perturbations

Abstract

We consider heat semigroups of the form $\exp(t(\Delta - \lambda\mathbf{1}_{\Omega_0}))$ on bounded domains. These singularly perturbed equations arise in certain models of diffusion limited chemical reactions. Using variants of Moser iteration, we show sub-exponential decay in the ``large coupling limit", i.e. as $\lambda\nearrow\infty$, in compact subdomains of the ``obstacle", $\Omega_0$.