Large-time asymptotics of the wave fronts length I The Euclidean disk

TL;DR

This paper investigates the long-term behavior of wave fronts in a Euclidean disk, providing a simplified proof of their linear asymptotics and calculating oscillating correction terms.

Contribution

It offers a shorter proof of the large-time asymptotics and computes oscillating corrections for wave fronts in a Euclidean disk.

Findings

Wave front length exhibits linear growth over large times.

Oscillating correction terms are explicitly computed.

Simplified proof enhances understanding of wave front asymptotics.

Abstract

In a previous work, the second author gives a formula showing thatthe wave frontissued of a point of the unit disk hasa large time linear asymptotics. In the present paper, we give ashorter proofand compute the oscillating corrections.