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On Some Problems for Partial Differential Equations with a Small Parameter in the Principal Part

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Abstract

In this paper, we consider problems for partial differential equations that contain a small parameter in the principal part. We construct exact solutions of the original singularly perturbed problems and, passing to the limit, we state a correspondence between these solutions and solutions of the limit problems obtained from the original problems if the small parameter is set equal to zero. Examples given in this paper show that among singularly perturbed problems for partial differential equations, there are problems that possess characteristic properties of regularly perturbed problems and allow constructing asymptotic solutions by methods of the theory of regular perturbations.

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Authors and Affiliations

  1. Irkutsk State University, Irkutsk, Russia

    I. V. Zakharova

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  1. I. V. Zakharova
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Correspondence to I. V. Zakharova.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 183, Differential Equations and Optimal Control, 2020.

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Zakharova, I.V. On Some Problems for Partial Differential Equations with a Small Parameter in the Principal Part. J Math Sci 279, 623–634 (2024). https://doi.org/10.1007/s10958-024-07043-x

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  • DOI: https://doi.org/10.1007/s10958-024-07043-x

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