A Riemann–Hilbert Type Problem for a Singularly Perturbed Cauchy–Riemann Equation with a Singularity in the Coefficient

We consider the Riemann–Hilbert problem for a singularly perturbed system of partial differential equations of the Cauchy–Riemann type. Using the Lomov regularization method, we obtain sufficient conditions under which the asymptotic solutions of the problem converge in the usual sense.

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Bibliographic Details
Published inDifferential equations Vol. 58; no. 3; pp. 367 - 380
Main Author Fedorov, Yu. S.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.03.2022
Springer
Springer Nature B.V
Subjects
Asymptotic methods
Cauchy-Riemann equations
Difference and Functional Equations
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Regularization
Regularization methods
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Summary:We consider the Riemann–Hilbert problem for a singularly perturbed system of partial differential equations of the Cauchy–Riemann type. Using the Lomov regularization method, we obtain sufficient conditions under which the asymptotic solutions of the problem converge in the usual sense.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266122030077