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Asymptotics of the Solution to the Roben Problem for a Ring with Regularly Singular Boundary

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Abstract

The aim of the research is the development of the asymptotic method of boundary functions to Robin problem for a ring with regularly singular boundary. This work is devoted to constructing complete asymptotic expansions of the solutions of Robin problem for singular perturbed inhomogeneous linear second order elliptic equation with regularly singular boundary. Singularities of the equation: the presence of a small parameter at the Laplace operator and the corresponding unperturbed (limit) the differential equation of first order has a singularity at the border ring. Bisingularly problems of the Robin studied in the ring. Full asymptotic expansion of the solution of bisingularly problems constructed by modification method of boundary functions. The resulting solutions are asymptotic in the sense Erdei. The resulting asymptotic expansions of the solutions of boundary value problems justified by the principle of maximum.

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Authors and Affiliations

  1. Department of Informatics, OSh State University, 723500, Osh, Kyrgyzstan

    D. A. Tursunov & M. O. Orozov

Authors
  1. D. A. Tursunov
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  2. M. O. Orozov
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Correspondence to D. A. Tursunov or M. O. Orozov.

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(Submitted by A. M. Elizarov)

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Tursunov, D., Orozov, M. Asymptotics of the Solution to the Roben Problem for a Ring with Regularly Singular Boundary. Lobachevskii J Math 41, 89–95 (2020). https://doi.org/10.1134/S1995080220010126

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  • DOI: https://doi.org/10.1134/S1995080220010126

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