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A generalization of Bitsadze–Samarskii problem for mixed type equation

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Abstract

We study a boundary-value problem with Bitsadze–Samarskii conditions on boundary characteristic on a special inner curve and on a segment of degeneration of mixed type equation. Its solvability is proved by method of integral equations, and uniqueness of solution is established by means of the maximum principle.

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References

  1. Bitsadze, A. V. and Samarskii, A. A. “On Some Simple Generalizations of Linear Elliptic Boundary Problems”, Sov.Math.Dokl. 10, 398–400 (1969).

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  2. Smirnov, M. M. Equations of Mixed Type (Vysshaya shkola, Moscow, 1985) [in Russian].

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  3. Bitsadze, A. V. Some Classes of Partial Differential Equations (Nauka, Moscow, 1981) [in Russian].

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  4. Mikhlin, S. G. “On F. Trikomi Integral Equation”, Dokl. Akad. Nauk SSSR 59, 197–199 (1948).

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Authors and Affiliations

  1. Termez State University, ul. F. Khodzhaeva, Termez, 190111, Republic of Uzbekistan

    M. Mirsaburov, I. N. Khairullaev & U. E. Bobomurodov

Authors
  1. M. Mirsaburov
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  2. I. N. Khairullaev
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  3. U. E. Bobomurodov
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Corresponding author

Correspondence to M. Mirsaburov.

Additional information

Original Russian Text © M. Mirsaburov, I.N. Khairullaev, U.E. Bobomurodov, 2016, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, No. 10, pp. 36–40.

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Mirsaburov, M., Khairullaev, I.N. & Bobomurodov, U.E. A generalization of Bitsadze–Samarskii problem for mixed type equation. Russ Math. 60, 29–32 (2016). https://doi.org/10.3103/S1066369X16100054

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  • DOI: https://doi.org/10.3103/S1066369X16100054

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