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A problem with tricomi and frankl conditions on the characteristic for a class of mixed-type equations

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Abstract

In this paper we prove the correctness of a problem with Tricomi and Frankl conditions on the characteristic for a certain class of mixed-type equations.

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References

  1. F. Tricomi, On Linear Differential Equations of the Second Order of Mixed Type (Gostekhizdat, Moscow-Leningrad, 1947) [Russ. transl.].

    Google Scholar 

  2. F. I. Frankl, “Subsonic Flow Past Profiles with Supersonic Zone Terminating with a Normal Shock,” Prikl. Mat. Mekh. 20(2), 196–202 (1956).

    MathSciNet  MATH  Google Scholar 

  3. Yu. V. Devingtal’, “The Existence and Uniqueness of the Solution of a Problem of F. I. Frankl,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 2, 39–51 (1958).

  4. Lin Tzian-bin, “On Some Problems of Frankl’,” Vestn. Leningradsk. Gos. Univ. Ser. Matem., Mekhan. i Astr. 3(13), 28–39 (1961).

    Google Scholar 

  5. M. S. Salakhitdinov and M. Mirsaburov, “A Problem with a Nonlocal Boundary Condition on the Characteristic for a Class of Equations of Mixed Type,” Matem. Zametki 86(5), 748–760 (2009).

    Article  MathSciNet  Google Scholar 

  6. M. M. Smirnov, Equations of Mixed Type (Nauka, Moscow, 1985) [in Russian].

    Google Scholar 

  7. M. S. Salakhitdinov and M. Mirsaburov, Nonlocal Problems for Mixed-Type Equations with Singular Coefficients (NUUz, Tashkent, 2005) [in Russian].

    Google Scholar 

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

    MATH  Google Scholar 

  9. S. G. Mikhlin, “On the F. Tricomi Integral Equation,” Sov. Phys. Dokl. 59(6), 1053–1056 (1948).

    Google Scholar 

  10. A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series (Nauka, Moscow, 1981) [in Russian].

    MATH  Google Scholar 

  11. F. D. Gakhov and Yu. I. Cherskii, Convolution Equations (Nauka, Moscow, 1978) [in Russian].

    MATH  Google Scholar 

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Authors and Affiliations

  1. Termez State University, ul. F. Khodzhaeva 43, Termez, 190102, Republic of Uzbekistan

    M. Mirsaburov & Zh. Khudzhaev

Authors
  1. M. Mirsaburov
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  2. Zh. Khudzhaev
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Corresponding author

Correspondence to M. Mirsaburov.

Additional information

Original Russian Text © M. Mirsaburov and Zh. Khudzhaev, 2013, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, No. 1, pp. 41–50.

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Mirsaburov, M., Khudzhaev, Z. A problem with tricomi and frankl conditions on the characteristic for a class of mixed-type equations. Russ Math. 57, 35–43 (2013). https://doi.org/10.3103/S1066369X13010040

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  • DOI: https://doi.org/10.3103/S1066369X13010040

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