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Volume 40, Issue 2
Analytic Regularity for a Singularly Perturbed Reaction-Convection-Diffusion Boundary Value Problem with Two Small Parameters

Irene Sykopetritou & Christos Xenophontos

Commun. Math. Res., 40 (2024), pp. 125-153.

Published online: 2024-05

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  • Abstract

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 the assumption of analytic input data. 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.

  • AMS Subject Headings

34E05, 34E10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-40-125, author = {Sykopetritou , Irene and Xenophontos , Christos}, title = {Analytic Regularity for a Singularly Perturbed Reaction-Convection-Diffusion Boundary Value Problem with Two Small Parameters}, journal = {Communications in Mathematical Research }, year = {2024}, volume = {40}, number = {2}, pages = {125--153}, abstract = {

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 the assumption of analytic input data. 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.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2023-0025}, url = {http://global-sci.org/intro/article_detail/cmr/23085.html} }
TY - JOUR T1 - Analytic Regularity for a Singularly Perturbed Reaction-Convection-Diffusion Boundary Value Problem with Two Small Parameters AU - Sykopetritou , Irene AU - Xenophontos , Christos JO - Communications in Mathematical Research VL - 2 SP - 125 EP - 153 PY - 2024 DA - 2024/05 SN - 40 DO - http://doi.org/10.4208/cmr.2023-0025 UR - https://global-sci.org/intro/article_detail/cmr/23085.html KW - Singularly perturbed problem, reaction-convection-diffusion, boundary layers, analytic regularity. AB -

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 the assumption of analytic input data. 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.

Sykopetritou , Irene and Xenophontos , Christos. (2024). Analytic Regularity for a Singularly Perturbed Reaction-Convection-Diffusion Boundary Value Problem with Two Small Parameters. Communications in Mathematical Research . 40 (2). 125-153. doi:10.4208/cmr.2023-0025
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