M. S. Salakhitdinov, N. B. Islamov, “Nonlocal boundary-value problem with Bitsadze–Samarskii condition for equation of parabolic-hyperbolic type of the second kind”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, Number 6,Pages <nobr>43

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Nonlocal boundary-value problem with Bitsadze–Samarskii condition for equation of parabolic-hyperbolic type of the second kind

M. S. Salakhitdinov^a, N. B. Islamov^b

^a Chair of Differential Equations, National University of Uzbekistan, Vuzgorodok, Tashkent, 100174 Republic of Uzbekistan
^b Chair of Higher Mathematics, Tashkent State Economic University, 49 Uzbekistan str., Tashkent, 100003 Republic of Uzbekistan

Abstract: We prove the unique solability of nonlocal boundary-value problem for a degenerate parabolic-hyperbolic equation of the second kind in the case when on the first part of a characteristic a nonlocal boundary condition is specified, while on parallel characteristic the Bitsadze–Samarskii condition is specified.

Keywords: degenerate parabolic-hyperbolic equation, nonlocal boundary-value problem, equation of the second kind, Bitsadze–Samarskii condition, uniqueness and existence of a solution, extremum principle, Fredholm integral equation.

UDC: 517.956

Received: 03.02.2014