Existence of a degenerate singularity in the high activation energy limit of a reaction-diffusion equation

G. S. Weiss, G. Zhang

We consider the singular perturbation problem $$\Delta u_{\epsilon }={\beta }_{\epsilon }(u_{\epsilon }),$$ where ${\beta }_{\epsilon }(s)=\frac{1}{\epsilon }\beta (\frac{s}{\epsilon })$, $\beta$ is a Lipschitz continuous function such that $\beta >0$ in $(0,1)$, $β\equi…