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A Bitsadze–Samarskii-Type Problem for a Second-Kind Mixed-Type Equation in a Domain with a Horizontal Half-Strip as Its Elliptic Part

Р.Т. ЗуннуновLaboratory of Mathematical Modeling of Nonlinear Processes, V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy, University Street 9, Tashkent 100174, UzbekistanRoman ParovikLaboratory of Modeling Physical Processes, Institute of Cosmophysical Research and Radio Wave Propagation Far Eastern Branch of the Russian Academy of Sciences, Mirnaya Street 7, Paratunka 684034, RussiaAkramkhon ErgashevDepartment of Mathematics, Kokand State University, Turon Street 23, Kokand 150100, Uzbekistan

Mathematicsjournal2026en

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Annotatsiya

In the theory of mixed-type equations, there are many works in bounded domains with smooth boundaries bounded by a normal curve for first- and second-kind mixed-type equations. In this paper, for a second-kind mixed-type equation in an unbounded domain whose elliptic part is a horizontal half-strip, a Bitsadze–Samarskii-type problem is investigated. The uniqueness of the solution is proved using the extremum principle, and the existence of the solution is proved by the Green’s function method and the integral equations method. When constructing the Green’s function, the properties of Bessel functions of the second kind with imaginary argument and the properties of the Gauss hypergeometric function are widely used. Visualization of the solution to the Bitsadze–Samarskii-type problem is performed, confirming its correctness from both mathematical and physical points of view.

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Mavzular

Differential Equations and Boundary Problems Algebraic and Geometric Analysis Analytic and geometric function theory

Identifikatorlar

DOI: 10.3390/math14030487

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