Analytic regularity for a singularly perturbed system of reaction-diffusion equations with multiple scales: proofs

Abstract

We consider a coupled system of two singularly perturbed reaction-diffusion equations, with two small parameters $0<\epsilon \le \mu \le 1$, each multiplying the highest derivative in the equations. The presence of these parameters causes the solution(s) to have \emph{boundary layers} which overlap and interact, based on the relative size of $\epsilon$ and . We construct full asymptotic expansions together with error bounds that cover the complete range $0<\epsilon \le \mu \le 1$. For the present case of analytic input data, we derive derivative growth estimates for the terms of the asymptotic expansion that are explicit in the perturbation parameters and the expansion order.

References in corpus (1)

• Analytic regularity for a singularly perturbed system of reaction-diffusion equations with multiple scales: proofs

Cited by in corpus (3)

• Robust exponential convergence of $hp$-FEM in balanced norms for singularly perturbed reaction-diffusion equations
• Analytic regularity for a singularly perturbed system of reaction-diffusion equations with multiple scales: proofs
• Analytic regularity for a singularly perturbed reaction-convection-diffusion boundary value problem with two small parameters