Boundary layer solutions to singularly perturbed quasilinear systems
type: Item
instance of: scholarly article
title: Boundary layer solutions to singularly perturbed quasilinear systems
author: V. F. Butuzov
author: Lutz Recke
author: N. N. Nefedov
author: Oleh Omel'chenko
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2022-10-25T00:00:00Z
review text: This paper considers weak boundary layer solutions to the singularly perturbed ODE systems of the type \[\varepsilon^2(A(x,u(x),\varepsilon)u'(x))'=f(x,u(x),\varepsilon).\] The new features are that the authors do not consider one scalar equation, but systems, where the systems are allowed to be quasilinear, and that the systems are spatially non-smooth. Although the results about existence, asymptotic behavior, local uniqueness and stability of boundary layer solutions are similar to those known for semilinear, scalar and smooth problems, there are at least three essential differences: 1) the asymptotic convergence rates valid for smooth problems are not true anymore, in general, in the non-smooth case; 2) a specific local uniqueness condition from the scalar case is not sufficient anymore in the vectorial case; 3) the monotonicity condition, which is sufficient for stability of boundary layers in the scalar case, must be adjusted to the vectorial case
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34E10
zbMATH DE Number: 7606638
zbMATH Keywords: quasilinear ODE system
zbMATH Keywords: singular perturbation
zbMATH Keywords: weak solution
zbMATH Keywords: asymptotic expansion
zbMATH Keywords: boundary layer
reviewed by: Dilmurat Abdillazhanovich Tursunov
MaRDI profile type: Publication
full work available at URL: dcdsb.2021226
OpenAlex ID: W3200314439
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DOI: 10.3934/DCDSB.2021226
description: scientific article; zbMATH DE number 7606638