Non Local Hyperbolic Dynamics of Clusters

TL;DR

This paper studies a non-local hyperbolic system modeling cluster dynamics, establishing well-posedness, stability, and qualitative properties, with implications for understanding cluster behavior and potential applications in encryption.

Contribution

It provides the first rigorous analysis of a non-local hyperbolic system for clusters, including well-posedness and stability, and explores qualitative solution properties.

Findings

Proved well-posedness of the non-local hyperbolic system.

Derived stability estimates for solutions.

Identified conditions for cluster fragmentation and independent development.

Abstract

The formation, movement and gluing of clusters can be described through a system of non local balance laws. Here, the well posedness of this system is obtained, as well as various stability estimates. Remarkably, qualitative properties of the solutions are proved, providing information on stationary solutions and on the propagation speed. In some cases, fragmentation leads to clusters developing independently. Moreover, these equations may serve as an encryption/decryption tool. This poses new analytical problems and asks for improved numerical methods.