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On a problem with shift for degenerate equation of mixed type

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Abstract

In this paper, for a class of mixed type equations we consider a problem with shift on a boundary characteristic. We prove theorems of uniqueness and existence of a solution to formulated problem.

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References

  1. Smirnov, M. M. Mixed Type Equations (Vysshaya Shkola, Moscow, 1985) [in Russian].

    Google Scholar 

  2. Zhegalov, V. I. “A Boundary-Value Problem for an Equation of Mixed Type with Boundary Conditions on Both Characteristics and with Discontinuities on the Transition Curve,” Uchen. Zap. Kazan. Gos. Univ. 122(3), 3–16 (1962).

    MATH  Google Scholar 

  3. Nakhushev, A. M. “On Some Boundary-Value Problems for Hyperbolic Equations and Mixed Type Equations,” Differents. Uravneniya 5(1), 44–59 (1969).

    MATH  Google Scholar 

  4. Kapustin, N. Yu., Sabitov, K.B. “Solution of a Problem in the Theory of the Frankl’ Problem for Equations of Mixed Type,” Differential Equations 27(1), 47–54 (1991).

    MATH  MathSciNet  Google Scholar 

  5. Sabitov, K. B., Isyangil’din, A. Kh. “A Tricomi-Type Problem with a Nonlocal Conjugation Condition for an Equation of Mixed Type,” Russian Acad. Sci. Dokl. Math. 46(2), 364–368 (1993).

    MathSciNet  Google Scholar 

  6. Sabitov, K. B., Isyangil’din, A. Kh. “A Tricomi Problem with a Nonlocal Conjugation Condition for the Generalized Tricomi Equation,” Differential Equations 32(3), 413–416 (1996).

    MATH  MathSciNet  Google Scholar 

  7. Salakhitdinov, M. S., Mirsaburov, M. Nonlocal Problems for Mixed Type Equations with Singular Coefficients (Tashkent, Universitet, Yangiyo’l Poligraf Servis, 2005).

    Google Scholar 

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

    MATH  Google Scholar 

  9. Mirsaburova, G. M. “AMixed Problem with Tricomi and Frankl Conditions for the Gellerstedt Equation with a Singular Coefficient,” Russian Mathematics (Iz. VUZ) 57(7), 13–26 (2013).

    MATH  MathSciNet  Google Scholar 

  10. Soldatov, A. P. “On the Noether Theory of Operators. One-Dimensional Singular Integral Operators of General Form,” Differentsial’nye Uravneniya 14(4), 706–718 (1978).

    MATH  MathSciNet  Google Scholar 

  11. Duduchava, R. V. Integral Equations of Convolution Type with Discontinuous Presymbols. Singular Integral Equations with Fixed Singularities, and their Applications to Problems of Mechanics (Mitsniereba, Tbilisi, 1978).

    Google Scholar 

  12. Polosin, A. A. “On the Unique Solvability of the Tricomi Problem for a Special Domain,” Differential Equations 32(3), 398–405 (1996).

    MATH  MathSciNet  Google Scholar 

  13. Mirsaburov, M. “A Boundary-Value Problem for a Class of Equations of Mixed Type with the Bitsadze-Samarskii Condition on Parallel Characteristics,” Differ. Equ. 37(9), 1349–1353 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  14. Mikhlin, S. G. “On Integral F. Trikomi Equation,” DAN SSSR 59(6), 1053–1056 (1948).

    Google Scholar 

  15. Sabitov, K. B., Bikkulova, G. G., Gimaltdinova, A. A. On the Theory of Mixed Type Equations with Two Lines of Change of Type (Gilem, Ufa, 2006).

    Google Scholar 

  16. Gakhov, F. D., Cherskii, Yu. I. Equations of Convolution Type (Nauka, Moscow, 1978) [in Russian].

    MATH  Google Scholar 

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Authors and Affiliations

  1. Termez State University, ul. F. Khodzhaeva 43, Termez, 190111, Republic of Uzbekistan

    M. Mirsaburov & S. T. Chorieva

Authors
  1. M. Mirsaburov
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  2. S. T. Chorieva
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Correspondence to M. Mirsaburov.

Additional information

Original Russian Text © M. Mirsaburov, S.T. Chorieva, 2015, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, No. 4, pp. 46–54.

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Mirsaburov, M., Chorieva, S.T. On a problem with shift for degenerate equation of mixed type. Russ Math. 59, 38–45 (2015). https://doi.org/10.3103/S1066369X15040052

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  • DOI: https://doi.org/10.3103/S1066369X15040052

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