Analytic regularity for a singularly perturbed system of reaction-diffusion equations with multiple scales: proofs
This provides rigorous analytic regularity results for multi-scale reaction-diffusion systems, which is important for numerical analysis and modeling of problems with overlapping boundary layers.
The paper constructs full asymptotic expansions with error bounds for a coupled system of two singularly perturbed reaction-diffusion equations with two small parameters, covering the entire parameter range. Derivative growth estimates explicit in perturbation parameters and expansion order are derived for analytic input data.
We consider a coupled system of two singularly perturbed reaction-diffusion equations, with two small parameters $0< ε\le μ\le 1$, 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 $ε$ and $% μ$. We construct full asymptotic expansions together with error bounds that cover the complete range $0 < ε\leq μ\leq 1$. 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.