B. I. Islomov, D. A. Nasirova, “A problem with gellerstedt conditions on different characteristics for a mixed loaded equation of the second kind”, Eurasian Math. J., 2024, Volume 15, Number 1,Pages <nobr>34

A problem with gellerstedt conditions on different characteristics for a mixed loaded equation of the second kind

B. I. Islomov^a, D. A. Nasirova^b

^a Department of Differential Equations and Mathematical Physics, National University of Uzbekistan named after M. Ulugbek, 4 University St, 100174, Tashkent, Uzbekistan
^b Department of Higher Mathematics, Tashkent State Technical University named after I. Karimov, Almazar district, 2 University St, 100095, Tashkent, Uzbekistan

Abstract: This work is devoted to a formulation and an investigation of a boundary value problem with Gellerstedt conditions on different characteristics for the loaded parabolic-hyperbolic type equation of the second kind.By using the extremum principle and the method of energy integrals, there are proved the uniqueness of solution of the formulated problem, and the existence of a solution to the problem — by the method integral equations.

Keywords and phrases: loaded equation of the second kind, problem with Gellerstedt conditions, representation of the general solutions, energy integral method, extremum principle, integral equation with a shift.

MSC: 35M10, 35M12, 35K15, 35L10, 35K10

Received: 26.06.2023

Language: English

DOI: 10.32523/2077-9879-2024-15-1-34-48