Asymptotic properties of solutions to the characteristic problem for the ultrahyperbolic equation

TL;DR

This paper investigates the smoothness and asymptotic behavior of solutions to the ultrahyperbolic equation with data on a characteristic hyperplane, focusing on their properties along characteristic lines.

Contribution

It provides new insights into the asymptotic properties and smoothness of solutions to the ultrahyperbolic equation with characteristic initial data.

Findings

Analyzes smoothness of solutions along characteristic lines.

Derives asymptotic behavior of solutions in Euclidean space.

Provides conditions for regularity of solutions on characteristic hyperplanes.

Abstract

The paper concerns the problem for the ultrahyperbolic equation in the Euclidean space with data on a characteristic hyperplane. Smoothness and asymptotics of the solution along characteristic lines transversal to the initial hyperplane are investigated.