Singular Perturbations in First-Order Partial Differential Equations with Matrix Differential Operators

Singular Perturbations in First-Order Partial Differential Equations with Matrix Differential Operators

In this paper, we consider differential equations whose degeneracy is due to the presence of a matrix differential operator coefficient of the derivative perturbed by a small parameter. Properties of this operator are applied to the analysis of the presence of a boundary layer in solutions of initia...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) Vol. 268; no. 1; pp. 130 - 137
Main Author: Uskov, V. I.
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01-11-2022
Springer
Springer Nature B.V
Subjects:
Analysis
Boundary layers
Boundary value problems
Differential equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Operators (mathematics)
Partial differential equations
Perturbation
small perturbation
first-order differential equation
boundary layer
parameter
35F40
matrix differential operator
Banach space
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Summary:In this paper, we consider differential equations whose degeneracy is due to the presence of a matrix differential operator coefficient of the derivative perturbed by a small parameter. Properties of this operator are applied to the analysis of the presence of a boundary layer in solutions of initial-boundary-value problems for equations considered. Regularity conditions of degeneracy are determined.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-022-06185-0