On a nonlocal problem for mixed parabolic–hyperbolic type equation with nonsmooth line of type changing
Erkinjon KarimovInstitute of Mathematics, National University of Uzbekistan named after Ulugbek, Tashkent, UzbekistanNilufar A. RakhmatullaevaTashkent State Technical University named after A. R. Beruni, Tashkent, Uzbekistan
ABI
Annotatsiya
In this paper, we investigate a boundary problem with nonlocal conditions for mixed parabolic–hyperbolic type equation with three lines of type changing. Considered domain contains a rectangle as a parabolic part and three domains bounded by smooth curves and type-changing lines as a hyperbolic part of the mixed domain. Applying method of energy integrals we prove the uniqueness of the solution for the considered problem. The proof of the existence will be done by reducing the original problem into the system of the second kind Volterra integral equations.
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