Abstract
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.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 172, Proceedings of the Voronezh Winter Mathematical School “Modern Methods of Function Theory and Related Problems,” Voronezh, January 28 – February 2, 2019. Part 3, 2019.
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Uskov, V.I. Singular Perturbations in First-Order Partial Differential Equations with Matrix Differential Operators. J Math Sci 268, 130–137 (2022). https://doi.org/10.1007/s10958-022-06185-0
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DOI: https://doi.org/10.1007/s10958-022-06185-0
Keywords and phrases
- Banach space
- matrix differential operator
- first-order differential equation
- small perturbation
- parameter
- boundary layer