Abstract
We prove theorems on the existence and uniqueness of solutions of nonlocal boundary-value problems with shift for mixed second- and third-order equations of hyperbolic-parabolic type.
References
A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics [in Russian] Nauka, Moscow 1966.
M. S. Salakhitdinov and A. K. Urinov, “On one boundary-value problem for an equation of mixed type with nonsmooth lines of degeneration,” Dokl. Akad. Nauk SSSR, 262, No. 3, 539–541 (1982).
H. Bateman and A. Erdelyi, Higher Transcendental Functions, Vol. 2, McGraw-Hill, New York (1953).
S. G. Samko, A. A. Kilbas, and O. I. Marichev, Integrals and Derivatives of Fractional Order and Their Applications [in Russian] Nauka i Tekhnika, Moscow 1987.
A. V. Bitsadze, Certain Classes of Partial Differential Equations [in Russian] Nauka, Moscow 1981.
S. K. Kumykova, “On one boundary-value problem with shift for the equation sgn y |y|m U xx + U yy = 0,” Differents. Uravn., 12, No. 1, 77–86(1976).
T. D. Dzhuraev, Boundary-Value Problems for Equations of Mixed and Combined Mixed Type [in Russian] Fan, Tashkent 1979.
V. A. Eleev and S. K. Kumykova, “On some boundary-value problems with shift for an equation of the third order,” in: Nonlinear Boundary-Value Problems of Mathematical Physics and Their Applications [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1993), pp. 52–54.
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Eleev, V.A., Kumykova, S.K. On some boundary-value problems with a shift on characteristics for a mixed equation of hyperbolic-parabolic type. Ukr Math J 52, 809–820 (2000). https://doi.org/10.1007/BF02487291
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DOI: https://doi.org/10.1007/BF02487291