A Note on Moser Iteration and the Large Coupling Limit

Abstract

We consider heat semigroups of the form $\exp (t(\hat{I}”-\hat{I}»1_{\hat{I}{\text{c◯}}_0}))$ 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 $\hat{I}»\nearrow \infty$, in compact subdomains of the ``obstacle", $\hat{I}{\text{c◯}}_0$.

8 pages. Submitted. Title changed and the exposition has been streamlined in this version. Comments and suggestions welcome