Abstract
For a mixed type equation of the second kind, we prove the uniqueness and existence of a solution of the boundary value problem with the Tricomi condition on part of the boundary characteristic and the Bitsadze–Samarskii condition on the boundary characteristic and on an internal characteristic parallel to it.
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REFERENCES
Tricomi, F., Sulla equazioni lineari alle derivate parziali di \(2^{\text {o}} \) ordine di tipo misto, Rome: R. Accad. Naz., 1923. Translated under the title: O lineinykh uravneniyakh v chastnykh proizvodnykh vtorogo poryadka smeshannogo tipa, Moscow–Leningrad: OGIZ, 1947.
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.
Karol’, I.L., On a boundary value problem for a mixed elliptic-hyperbolic type equation, Dokl. Akad. Nauk SSSR, 1953, vol. 88, no. 2, pp. 197–200.
Smirnov, M.M., Uravneniya smeshannogo tipa (Equations of Mixed Type), Moscow: Vyssh. Shkola, 1985.
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, 2005.
Salakhitdinov, M.S. and Islamov, N.B., A nonlocal boundary-value problem with the Bitsadze–Samarskii condition for a parabolic-hyperbolic equation of the second kind, Russ. Math., 2015, vol. 59, pp. 34–42.
Islamov, N.B., Analogue of Bitsadze–Samarskii problem for a class of parabolic-hyperbolic equations of second kind, Ufa Math. J., 2015, vol. 7, no. 1, pp. 31–45.
Bitsadze, A.V., Nekotorye klassy uravnenii v chastnykh proizvodnykh (Some Classes of Partial Differential Equations), Moscow: Nauka, 1981.
Sabitov, K.B., Formulation of boundary-value problems for an equation of mixed type with degeneracy of second kind on the boundary of an infinite domain, Sib. Math. J., 1980, vol. 21, no. 4, pp. 591–594.
Khairullin, R.S., On the Tricomi problem for a mixed-type equation of the second kind, Sib. Math. J., 1994, vol. 35, no. 4, pp. 826–834.
Mikhlin, S.G., On the integral F. Tricomi equation, Dokl. Akad. Nauk SSSR, 1948, vol. 59, no. 6, pp. 1053–1056.
Polosin, A.A., Unique solvability of the Tricomi problem for a special domain, Differ. Equations, 1996, vol. 32, no. 3, pp. 398–405.
Fikhtengol’ts, G.M., Osnovy matematicheskogo analiza. T. 2 (Fundamentals of Mathematical Analysis. Vol. 2), Moscow: Nauka, 1968.
Gakhov, F.D. and Cherskii, Yu.I., Uravneniya tipa svertki (Convolution Type Equations), Moscow: Nauka, 1978.
Gradshtein, I.S. and Ryzhik, I.M., Tablitsy integralov, summ, ryadov i proizvedenii (Tables of Integrals, Sums, Series, and Products), Moscow: Nauka, 1971.
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Translated by V. Potapchouck
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Mirsaburov, M., Islomov, N.B. Problem with a Bitsadze–Samarskii Condition on Parallel Characteristics for a Mixed Type Equation of the Second Kind. Diff Equat 57, 1358–1371 (2021). https://doi.org/10.1134/S0012266121100104
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DOI: https://doi.org/10.1134/S0012266121100104