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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Published in:Differential equations 2022-03, Vol.58 (3), p.367-380
Main Author: Fedorov, Yu. S.
Format: Article
Language:English
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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description 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.
doi_str_mv 10.1134/S0012266122030077
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subjects Asymptotic methods
Cauchy-Riemann equations
Difference and Functional Equations
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Regularization
Regularization methods
title A Riemann–Hilbert Type Problem for a Singularly Perturbed Cauchy–Riemann Equation with a Singularity in the Coefficient
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