| Issue |
Math. Model. Nat. Phenom.
Volume 20, 2025
|
|
|---|---|---|
| Article Number | 10 | |
| Number of page(s) | 28 | |
| Section | Mathematical methods | |
| DOI | https://doi.org/10.1051/mmnp/2025011 | |
| Published online | 16 April 2025 | |
Non-local hyperbolic dynamics of clusters
1
Unità INdAM & Dipartimento di Ingegneria dell’Informazione, Università di Brescia, Italy
2
Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Italy
* Corresponding author: rinaldo.colombo@unibs.it
Received:
12
September
2024
Accepted:
12
March
2025
The formation, movement and gluing of clusters can be described through a system of nonlocal conservation 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.
Mathematics Subject Classification: 35L65 / 91C20
Key words: Conservation laws / macroscopic modeling of clusters dynamics / pattern formation / hyperbolic encryption/decryption flows
© The authors. Published by EDP Sciences, 2025
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