We prove the unique solvability and obtain the explicit expression for the classical solution of mixed problem in a cylindrical domain for one class of multidimensional hyperbolic-parabolic equations.
References
O. A. Ladyzhenskaya, Mixed Problem for Hyperbolic Equations [in Russian], Gostekhizdat, Moscow (1953).
O. A. Ladyzhenskaya, Boundary-Value Problems of Mathematical Physics [in Russian], Nauka, Moscow (1973).
S. A. Aldashev, “Well-posedness of mixed problems for multidimensional hyperbolic equations with wave operator,” Ukr. Mat. Zh., 69, No. 7, 992–999 (2017); English translation: Ukr. Math. J., 69, No. 7, 1154–1163 (2017).
S. G. Mikhlin, Multidimensional Singular Integrals and Integral Equations [in Russian], Fizmatgiz, Moscow (1962).
S. A. Aldashev, “On the Darboux problems for one class of multidimensional hyperbolic equations,” Differents. Uravn., 34, No. 1, 64–68 (1998).
E. Kamke, Differentialgleichungen Lösungsmethoden und Lösungen, Akademische Verlagsgesellschaft Geest, Leipzig (1959).
H. Bateman and A. Erdélyi, Higher Transcendental Functions, Vol. 2, McGraw-Hill, New York (1954).
A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis [in Russian], Nauka, Moscow (1976).
A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1966).
S. A. Aldashev, “Well-posedness of the Dirichlet problem for one class of multidimensional hyperbolic-parabolic equations,” Ukr. Mat. Vestn., 10, No. 2, 147–157 (2013).
V. I. Smirnov, A Course in Higher Mathematics [in Russian], Vol. 4, Nauka, Moscow (1981).
A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs (1964).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, No. 2, pp. 280–288, February, 2020.
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Aldashev, S.A. Well-Posedness of a Mixed Problem in a Cylindrical Domain for One Class of Multidimensional Hyperbolic-Parabolic Equations. Ukr Math J 72, 317–326 (2020). https://doi.org/10.1007/s11253-020-01783-0
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DOI: https://doi.org/10.1007/s11253-020-01783-0