Abstract
We study a boundary-value problem with shift formixed-type equation of the third order. In the hyperbolic field boundary condition contains a linear combination of generalized operators of fractional integro-differentiation. We prove a unique solvability of the problem.
Similar content being viewed by others
References
Saigo, M. “A Remark on Integral Operators Involving the Gauss Hypergeometric Function,” Math. Rep. Kyushu Univ. 11, No. 2, 135–143 (1978).
Samko, S. G., Kilbas, A. A., Marichev, O. I. Fractional Integrals and Derivatives: Theory and Applications (Nauka i Tekhnika, Minsk, 1987) [in Russian].
Repin, O. A. Boundary-Value Problems with Shift for Equations ofHyperbolic andMixed Type (Saratov Univ. Press, 1992) [in Russian].
Eleev, V. A., Kumykova, S. K. “Interior-Boundary Value Problem for Mixed Type Equation of the ThirdOrder with Multiple Characteristics,” Izv. Kabardino-Balkarsk. Nauchn. tsentra RAN, No. 5(37), part 2, 5–14 (2010).
Repin, O. A., Kumykova, S. K. “Nonlocal Problem for an Equation of Mixed Type of Third Order with Generalized Operators of Fractional Integro-Differentiation of an Arbitrary Order,” Vestn. Samarsk. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, No. 4(25), 25–36 (2011).
Repin, O. A., Kumykova, S. K. “Problem with Shift for the Third-Order Equation with Discontinuous Coefficients,” Vestn. Samarsk. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, No. 4(29), 17–25 (2012).
Smirnov, M. M. Equations ofMixed Type (Nauka, Moscow, 1970) [in Russian].
Kumykova, S. K. “On a Shift Problem for the Equation sign y|y|muxx + uyy = 0,” Differents. Uravnen. 12, No. 1, 79–88 (1976). (Russian).
Tricomi, F. Lezioni Sulle Equazioni a Derivate Parziali Corso di Analisi Superiore (Torino, Gheroni, 1954; In. Lit.,Moscow, 1957).
Irgashev, Yu. “Some Boundary-Value Problems for Third Order Equations with Multiple Characteristics,” in Boundary-Value Problems for Differential Equations and their Applications (Fan, Tashkent, 1976), pp. 17–27.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © O.A. Repin, S.K. Kumykova, 2015, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, No. 7, pp. 49–57.
About this article
Cite this article
Repin, O.A., Kumykova, S.K. Boundary-value problem with saigo operators for mixed type equation of the third order with multiple characteristics. Russ Math. 59, 44–51 (2015). https://doi.org/10.3103/S1066369X15070051
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1066369X15070051