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We consider a coupled system of two singularly perturbed reaction-diffusionequations, with two small parameters $0< \epsilon \le \mu \le 1$, eachmultiplying the highest derivative in the equations. The presence of theseparameters causes the solution(s) to have \emph{boundary layers} which overlapand interact, based on the relative size of $\epsilon$ and $% \mu$. Weconstruct full asymptotic expansions together with error bounds that cover thecomplete range $0 < \epsilon \leq \mu \leq 1$. For the present case of analyticinput data, we derive derivative growth estimates for the terms of theasymptotic expansion that are explicit in the perturbation parameters and theexpansion order.

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