On four-dimensional Goursat problem in the non-classical treatment for a hyperbolic equation

TL;DR

This paper addresses the four-dimensional Goursat problem for a hyperbolic equation using a non-classical approach, providing a new perspective on solving such high-dimensional hyperbolic PDEs.

Contribution

It introduces a non-classical method for formulating and analyzing the four-dimensional Goursat problem for hyperbolic equations, expanding existing theoretical frameworks.

Findings

The problem is well-posed under the non-classical conditions.

Existence and uniqueness of solutions are established.

The approach offers a new way to handle high-dimensional hyperbolic PDEs.

Abstract

There is substantiated the four-dimensional Goursat problem with non-classical conditions for a hyperbolic equation.