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Gevrey problem for a loaded mixed parabolic equation with a fractional derivative. (English. Russian original) Zbl 1450.35266

J. Math. Sci., New York 250, No. 5, 746-752 (2020); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 149, 31-37 (2018).
Summary: In this paper, we consider the Gevrey problem for a loaded parabolic equation with the direct and reverse time in an unbounded domain. The problem on the solvability of this problem is reduced to the problem on the solvability of a generalized Abel equation in the class of function satisfying the Hölder condition.

MSC:

35R11 Fractional partial differential equations
35M13 Initial-boundary value problems for PDEs of mixed type
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[1] Gakhov, FD, Boundary-Value Problems (1990), New York: Dover, New York · Zbl 0830.30026
[2] Gekkieva, SK, The Gevrey problem for a fractional mixed parabolic equation, Izv. Kabardino-Balkar. Nauch. Tsentra Ross. Akad. Nauk, 76, 2, 38-43 (2017)
[3] S. Kh. Gekkieva, “Mixed boundary-value problems for a loaded diffusion-wave equation,” Nauch. Ved. Belgorod. Univ. Ser. Mat. Fiz., 42, No. 6 (227), 32-35 (2016).
[4] Gevrey, M., Sur les equations aux derives partielles du type parabolique, J. Math. Appl., 9, 6, 305-475 (1913)
[5] Kerefov, AA, The Gevrey problem for one mixed-parabolic equation, Differ. Uravn., 13, 1, 76-83 (1977) · Zbl 0338.35048
[6] Kerefov, AA, On a Gevrey boundary-value problem for a parabolic equation with a first-order alternating discontinuity of the coefficient of the time derivative, Differ. Uravn., 10, 1, 69-77 (1974) · Zbl 0271.35039
[7] N. V. Kislov and A. V. Chervyakov, “A boundary-value problem with alternating direction of time,” Vestn. Mosk. Energ. Inst., No. 6, 62-67 (2002).
[8] Nakhushev, AM, Problems with Shift for Partial Differential Equations [in Russian] (2006), Moscow: Nauka, Moscow · Zbl 1135.35002
[9] Nakhushev, AM, Loaded Equations and Their Applications [in Russian] (2012), Moscow: Nauka, Moscow
[10] Nakhushev, AM, Equations of Mathematical Biology [in Russian] (1995), Moscow: Vysshaya Shkola, Moscow · Zbl 0991.35500
[11] Popov, SV, On the first boundary-value problem for a parabolic equation with alternating direction of time, Dinam. Splosh. Sredy, 102, 100-113 (1991) · Zbl 0826.35045
[12] Pskhu, AV, Fractional Partial Differential Equations [in Russian] (2005), Moscow: Nauka, Moscow · Zbl 1193.35245
[13] Samko, SG; Kilbas, AA; Marichev, OI, Fractional Integrals and Derivatives and Their Applications [in Russian] (1987), Minsk: Nauka i Tekhnika, Minsk · Zbl 0617.26004
[14] Serbina, LI, Nonlocal Mathematical Models of Transport in Aquifer Systems [in Russian] (2007), Moscow: Nauka, Moscow · Zbl 1157.76001
[15] Tersenov, SA, Parabolic Equations with Alternating Direction of Time [in Russian] (1985), Moscow: Nauka, Moscow
[16] E. A. Zarubin, “On the uniqueness of a solution to the Gevrey problem for a fractional mixed diffusion equation,” in: Modern Methods in the Theory of Boundary-Value Problems [in Russian], Proc. Voronezh. Spring Math. School “Pontryagin Readings-XV,” Voronezh (2004), pp. 93-94.
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