Geodesic
Unique Solvability of an Analog of the Tricomi Problem with Nonlocal Integral Conjugation Condition
Matematičeskie zametki, Tome 87 (2010) no. 6, pp. 867-876 Cet article a éte moissonné depuis la source Math-Net.Ru

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Using an alternating method of Schwartz type, we prove the unique solvability of the elliptic-hyperbolic equation in the class of generalized solutions of an analog of the Tricomi problem with nonlocal integral conjugation condition for the case of an arbitrary approach of the elliptic boundary of the domain to the line of type change with the exception of the case of tangency.
Keywords: elliptic-hyperbolic equation, Tricomi problem, alternating method of Schwartz type, Riemann function, maximum principle.
Mots-clés : Goursat problem 
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     title = {Unique {Solvability} of an {Analog} of the {Tricomi} {Problem} with {Nonlocal} {Integral} {Conjugation} {Condition}},
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E. R. Mansurova. Unique Solvability of an Analog of the Tricomi Problem with Nonlocal Integral Conjugation Condition. Matematičeskie zametki, Tome 87 (2010) no. 6, pp. 867-876. http://geodesic.mathdoc.fr/item/MZM_2010_87_6_a7/

[1] V. F. Volkodavov, O. Yu. Naumov, “Dlya uravneniya smeshannogo tipa zadacha $\mathrm T$ s sopryazheniem spetsialnogo vida”, Neklassicheskie uravneniya matematicheskoi fiziki, In-t matem. SO RAN, Novosibirsk, 2002, 41–49 | Zbl

[2] V. F. Volkodavov, Yu. A. Ilyushina, “Dlya uravneniya smeshannogo tipa edinstvennost resheniya zadachi $T$ s sopryazheniem proizvodnoi po normali s drobnoi proizvodnoi”, Izv. vuzov. Matem., 2003, no. 9, 6–9 | MR | Zbl

[3] A. V. Bitsadze, Nekotorye klassy uravnenii v chastnykh proizvodnykh, Nauka, M., 1981 | MR | Zbl

[4] K. I. Babenko, “O zadache Trikomi”, Dokl. AN SSSR, 291:1 (1986), 14–19 | MR

[5] A. A. Kosovets, “Razreshimost zadachi Trikomi dlya odnogo uravneniya smeshannogo tipa”, Differents. uravneniya, 21:9 (1985), 1627–1628 | MR | Zbl

[6] K. B. Sabitov, “Alterniruyuschii metod tipa Shvartsa v teorii uravnenii smeshannogo tipa”, Dokl. RAN, 322:3 (1992), 476–480 | MR | Zbl

[7] S. L. Sobolev, Uravneniya matematicheskoi fiziki, Nauka, M., 1992 | MR | Zbl

[8] V. F. Volkodavov, M. E. Lerner, N. Ya. Nikolaev, V. A. Nosov, Tablitsy nekotorykh funktsii Rimana, integralov i ryadov, Izd-vo KGPI, Kuibyshev, 1982

[9] E. R. Mansurova, “K voprosu suschestvovaniya analoga zadachi Trikomi dlya uravneniya smeshannogo tipa s nelokalnym integralnym usloviem sopryazheniya”, Trudy mezhdunarodnoi konferentsii “Differentsialnye uravneniya i smezhnye problemy” posvyaschennoi yubileyu akademika Vladimira Aleksandrovicha Ilina, v. 2, Gilem, Ufa, 2008, 111–117