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Boundary Value Problems for Quasi-Hyperbolic Equations with Degeneration

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Abstract

The paper deals with the solvability analysis of boundary value problems for degenerate higher-order quasi-hyperbolic equations. The problems in question have the specific feature that the manifolds on which the equations characteristically degenerate are not freed from carrying boundary data. The aim of this paper is to prove the existence and uniqueness of regular solutions of the problems under study, that is, solutions all of whose generalized derivatives occurring in the corresponding equations exist as generalized derivatives in the sense of Sobolev.

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Notes

  1. Formally, the papers [4] and [5] deal with Eq. (0.2) for \(p=1\), but the methods proposed there were then successfully used in the solvability analysis of boundary value problems for Eq. (0.2) in the case of \(p>1\).

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Novosibirsk, 630090, Russia

    A. I. Kozhanov

  2. Academy of Sciences of the Republic of Sakha (Yakutia), Yakutsk, 677007, Russia

    A. I. Kozhanov

  3. Ammosov North-Eastern Federal University, Yakutsk, 677000, Russia

    N. R. Spiridonova

Authors
  1. A. I. Kozhanov
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  2. N. R. Spiridonova
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Correspondence to A. I. Kozhanov.

Additional information

Translated from Matematicheskie Zametki, 2022, Vol. 112, pp. 825–838 https://doi.org/10.4213/mzm13523.

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Kozhanov, A.I., Spiridonova, N.R. Boundary Value Problems for Quasi-Hyperbolic Equations with Degeneration. Math Notes 112, 911–921 (2022). https://doi.org/10.1134/S0001434622110256

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  • DOI: https://doi.org/10.1134/S0001434622110256

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