Short Communication
Differential Equations and Mathematical Physics

The nonlocal problem for a non-stationary third order composite type equation with general boundary condition

A. R. Khashimov

Tashkent Financial Institute, Tashkent, 100000, Uzbekistan

Abstract: We consider a nonlocal boundary value problem for non-stationary composite type equation of the third order. The values of function and its derivatives up to the second order on the boundary are given as a linear combination. The initial conditions are nonlocal. We prove the unique solvability for this problem. In proving the problem solution uniqueness we use the method of energy integrals and the theory of quadratic forms. For the problem solution construction we use the potential theory and Volterra integral equations. Some asymptotic properties of the fundamental solutions of the equation are studied.

Keywords: non-stationary equations, fundamental solutions, boundary value problem, potential theory, energy integral method, third order equations, composite type equations, system of integral equations, nonlocal problem.

UDC: 517.956

MSC: 35M10

Received: October 24, 2018
Revised: August 22, 2019
Accepted: January 27, 2020
First online: April 6, 2020

DOI: 10.14498/vsgtu1657

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