Differential Equations

, Volume 55, Issue 8, pp 1084–1093 | Cite as

Generalization of the Tricomi Problem

  • M. MirsaburovEmail author
  • O. Begaliev
  • N. Kh. KhurramovEmail author
Partial Differential Equations


For the equation (sgn y)|y|muxx + uyy +(β0/y)uy = 0 in a mixed domain, we prove existence and uniqueness theorems for a solution of the problem with the Tricomi condition on part of the boundary characteristic and the Gellerstedt condition on an internal characteristic parallel to it.


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  1. 1.
    Smirnov, M.M., Uravneniya smeshannogo tipa (Mixed Type Equations), Moscow: Nauka, 1985.Google Scholar
  2. 2.
    Salakhitdinov, M.S. and Mirsaburov, M., Nelokal’nye zadachi dlya uravnenii smeshannogo tipa s singulyarnymi koeffitsientami (Nonlocal Problems for Equations of Mixed Type with Singular Coefficients), Tashkent: Universitet, Yangiyo’l Poligraf Servis, 2005.Google Scholar
  3. 3.
    Nakhushev, A.M., On some boundary value problems for hyperbolic equations and equations of mixed type, Differ. Uravn., 1969, vol. 5, no. 1, pp. 44–59.Google Scholar
  4. 4.
    Bitsadze, A.V., Nekotorye klassy uravnenii v chastnykh proizvodnykh (Some Classes of Partial Differential Equations), Moscow: Nauka, 1981.zbMATHGoogle Scholar
  5. 5.
    Polosin, A.A., On the unique solvability of the Tricomi problem for a special domain, Differ. Equations, 1996, vol. 32, no. 3, pp. 398–405.MathSciNetzbMATHGoogle Scholar
  6. 6.
    Mirsaburov, M., A boundary value problem for a class of mixed equations with the Bitsadze–Samarskii condition on parallel characteristics, Differ. Equations, 2001, vol. 37, no. 9, pp. 1349–1353.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Mikhlin, S.G., On the integral F. Tricomi equation, Dokl. Akad. Nauk SSSR, 1948, vol. 59, no. 6, pp. 1053–1056.Google Scholar
  8. 8.
    Mirsaburov, M., Problem with analogs of the Frankl’ condition on a characteristic and the degeneration segment for an equation of mixed type with a singular coefficient, Differ. Equations, 2017, vol. 53, no. 6, pp. 773–783.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Fikhtengol’ts, G.M., Osnovy matematicheskogo analiza (Basics of Calculus), Moscow: Nauka, 1968, Vol. 2.Google Scholar
  10. 10.
    Gakhov, F.D. and Cherskii, Yu.I., Uravneniya tipa svertki (Convolution Type Equations), Moscow: Nauka, 1978.Google Scholar
  11. 11.
    Grandshtein, N.S. and Ryzhik, I.M., Tablitsy integralov, summ, ryadov i proizvedenii (Tables of Integrals, Sums, Series, and Products), Moscow, 1971.Google Scholar

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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Termez State UniversityTermez, Surkhandar’inskaya oblastUzbekistan

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