2019/01/27 by Irene Sykopetritou, Sykopetritou, Irene, Christos Xenophontos +1
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Material Science and Thermodynamics
paper · pdf · doi:10.48550/arxiv.1901.09397
openalex publication_date 2019/01/27 · openalex created_date 2023/11/01 · openalex updated_date 2026/07/28
We consider a second order, two-point, singularly perturbed boundary value problem, of reaction-convection-diffusion type with two small parameters, and we obtain regularity results for its solution. First we establish classical differentiability bounds that are explicit in the order of differentiation and the singular perturbation parameters. Next, for small values of these parameters we show that the solution can be decomposed into a smooth part, boundary layers at the two endpoints and a negligible remainder. Derivative estimates are obtained for each component of the solution, which again are explicit in the differentiation order and the singular perturbation parameters.