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Boundary Problems for Parabolic Equations with Degenerate Boundary Condition of the Third Kind

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Abstract

The solvability of initial-boundary value problems for linear parabolic equations of the second order with a degenerate boundary value condition of the third kind is studied. Sufficient conditions for the existence and uniqueness of solutions are given. It is shown that the degeneration effect can lead to nonuniqueness of solutions in the space \(W_{2}^{{2,1}}\).

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REFERENCES

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Funding

This work was supported by the Mathematical Center in Akademgorodok, agreement no. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation.

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Authors and Affiliations

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

    A. I. Kozhanov & A. N. Artyushin

  2. Novosibirsk State University, Novosibirsk, Russia

    V. V. Shubin

Authors
  1. A. I. Kozhanov
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  2. A. N. Artyushin
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  3. V. V. Shubin
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Corresponding authors

Correspondence to A. I. Kozhanov, A. N. Artyushin or V. V. Shubin.

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The authors declare that they have no conflicts of interest.

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Translated by I. Ruzanova

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Kozhanov, A.I., Artyushin, A.N. & Shubin, V.V. Boundary Problems for Parabolic Equations with Degenerate Boundary Condition of the Third Kind. Dokl. Math. 105, 106–108 (2022). https://doi.org/10.1134/S1064562422020144

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  • DOI: https://doi.org/10.1134/S1064562422020144

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