Singular perturbation analysis of a stationary diffusion/reaction system whose solution exhibits a corner-type behavior in the interior of the domain

Leonid V. Kalachev; Thomas I. Seidman

doi:10.1016/j.jmaa.2003.09.024

Singular perturbation analysis of a stationary diffusion/reaction system whose solution exhibits a corner-type behavior in the interior of the domain

Leonid V. Kalachev, Thomas I. Seidman

University of Maryland, Baltimore

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

We consider a singularly perturbed system of second-order differential equations describing steady state of a chemical process that involves three species, two reactions (one of which is fast), and diffusion. Formal asymptotic expansion of the solution is constructed in the case when solution exhibits a corner-type behavior in the interior of the domain of interest. The theorem on estimation of the remainder is proved using a fixed point argument.

Original language	English
Pages (from-to)	722-743
Number of pages	22
Journal	Journal of Mathematical Analysis and Applications
Volume	288
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2003.09.024
State	Published - Dec 15 2003

Keywords

Boundary function method
Corner-type behavior
Rate of convergence
Singular perturbation

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10.1016/j.jmaa.2003.09.024

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abstract = "We consider a singularly perturbed system of second-order differential equations describing steady state of a chemical process that involves three species, two reactions (one of which is fast), and diffusion. Formal asymptotic expansion of the solution is constructed in the case when solution exhibits a corner-type behavior in the interior of the domain of interest. The theorem on estimation of the remainder is proved using a fixed point argument.",

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AU - Kalachev, Leonid V.

AU - Seidman, Thomas I.

PY - 2003/12/15

Y1 - 2003/12/15

N2 - We consider a singularly perturbed system of second-order differential equations describing steady state of a chemical process that involves three species, two reactions (one of which is fast), and diffusion. Formal asymptotic expansion of the solution is constructed in the case when solution exhibits a corner-type behavior in the interior of the domain of interest. The theorem on estimation of the remainder is proved using a fixed point argument.

AB - We consider a singularly perturbed system of second-order differential equations describing steady state of a chemical process that involves three species, two reactions (one of which is fast), and diffusion. Formal asymptotic expansion of the solution is constructed in the case when solution exhibits a corner-type behavior in the interior of the domain of interest. The theorem on estimation of the remainder is proved using a fixed point argument.

KW - Boundary function method

KW - Corner-type behavior

KW - Rate of convergence

KW - Singular perturbation

UR - https://www.scopus.com/pages/publications/0346343158

U2 - 10.1016/j.jmaa.2003.09.024

DO - 10.1016/j.jmaa.2003.09.024

M3 - Article

AN - SCOPUS:0346343158

SN - 0022-247X

VL - 288

SP - 722

EP - 743

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Singular perturbation analysis of a stationary diffusion/reaction system whose solution exhibits a corner-type behavior in the interior of the domain

Abstract

Keywords

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