Analytic Regularity for a Singularly Perturbed Reaction-Convection-Diffusion Boundary Value Problem with Two Small Parameters (Communications in Mathematical Research, 2024)
We consider a second order, two-point, singularly perturbed boundary value problem, of reaction-convection-diffusion type with two small parameters, and we obtain analytic regularity results for its solution, under theassumption of analytic input data. First, we establish classical differentiabilitybounds that are explicit in the order of differentiation and the singular perturbation parameters. Next, for small values of these parameters we show thatthe solution can be decomposed into a smooth part, boundary layers at the twoendpoints, and a negligible remainder. Derivative estimates are obtained foreach component of the solution, which again are explicit in the differentiationorder and the singular perturbation parameters.
Keywords: Singularly perturbed problem; reaction-convection-diffusion; boundary layers; analytic regularity.