Article

On a Boundary Value Problem for a Class of Equations of Mixed Type

M. Kh. RuzievRomanovskii Institute of Mathematics, Academy of Sciences of Uzbekistan, 100174, Tashkent, UzbekistanN. T. YuldashevaRomanovskii Institute of Mathematics, Academy of Sciences of Uzbekistan, 100174, Tashkent, Uzbekistan

Lobachevskii Journal of Mathematicsjournal2023en

ABI

Abstract

In this paper we study a nonlocal boundary value problem for Gellerstedt equation with singular coefficient in an unbounded domain. The uniqueness of the solution to the problem is proved using the extremum principle. The existence of a solution to the problem is proved by the method of integral equations. The problem is equivalently reduced to solving a singular integral equation. We find its solution using the Carleman–Vekua method. Then, we get the Wiener–Hopf singular integral equation, and with the help of the Fourier transform it can be reduced to the Riemann boundary value problem.

Topics

Differential Equations and Boundary Problems Differential Equations and Numerical Methods Numerical methods for differential equations

Identifiers

DOI: 10.1134/s1995080223070399

Citations and references

Cited by 6 21 references

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