On the Volterra property of a boundary problem with integral gluing condition for mixed parabolic-hyperbolic equation

TL;DR

This paper investigates a boundary value problem with integral gluing conditions for a mixed parabolic-hyperbolic equation, proving it possesses the Volterra property using integral equations and functional analysis techniques.

Contribution

It establishes the Volterra property for a new class of boundary problems with integral gluing conditions in mixed parabolic-hyperbolic equations.

Findings

The problem has the Volterra property.

Method of integral equations is effective for such problems.

Functional analysis techniques are applied successfully.

Abstract

In the present work we consider a boundary value problem with gluing conditions of integral form for parabolic-hyperbolic type equation. We prove that the considered problem has the Volterra property. The main tools used in the work are related to the method of the integral equations and functional analysis.