On a non-local problem for parabolic-hyperbolic equation with three lines of type changing

TL;DR

This paper studies a boundary problem involving a parabolic-hyperbolic equation with three lines of type change, using non-local conditions and reducing it to Volterra integral equations of the second kind.

Contribution

It introduces a novel boundary problem with non-local conditions for a complex equation with changing type, and provides an equivalent integral equation formulation.

Findings

Reduction to Volterra integral equations of the second kind

Establishment of conditions for solvability

Analysis of the problem's well-posedness

Abstract

In the present work we investigate a boundary problem with non-local conditions, connecting values of seeking function on various characteristics for parabolic-hyperbolic equation with three lines of type changing. The considered problem is equivalently reduced to the system of Volterra integral equations of the second kind.