On the existence of eigenvalues of a boundary value problem with transmitting condition of the integral form for parabolic-hyperbolic equation

TL;DR

This paper investigates the eigenvalues of a boundary value problem involving a mixed parabolic-hyperbolic equation with an integral transmitting condition, establishing conditions for solvability and eigenvalue existence.

Contribution

It introduces new theorems proving strong solvability and eigenvalue existence for a boundary value problem with integral transmitting conditions in mixed parabolic-hyperbolic equations.

Findings

Proved strong solvability of the problem

Established existence of eigenvalues

Analyzed boundary conditions of integral form

Abstract

In the paper, we investigate a local boundary value problem with transmitting condition of the integral form for mixed parabolic-hyperbolic equation with non-characteristic line of type changing. Two theorems on strong solvability and the existence of eigenvalues of the considered problem have been proved.