Equipartition of energy for the wave equation associated to the Dunkl-Cherednik Laplacian

TL;DR

This paper studies the energy distribution of the wave equation linked to the Dunkl-Cherednik Laplacian, proving energy conservation, conditions for energy equipartition, and its asymptotic behavior.

Contribution

It introduces new results on energy properties specific to the wave equation involving the Dunkl-Cherednik Laplacian, including conservation and equipartition phenomena.

Findings

Total energy is conserved.

Strict energy equipartition occurs under certain conditions.

Asymptotic energy equipartition is established in general cases.

Abstract

This paper is concerned with energy properties of the wave equation associated to the Dunkl-Cherednik Laplacian. We establish the conservation of the total energy, the strict equipartition of energy under suitable assumptions and the asymptotic equipartition in the general case.