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.
Colombo, R., Garavello, M. (2025). Non-local hyperbolic dynamics of clusters. MATHEMATICAL MODELLING OF NATURAL PHENOMENA, 20, 1-28 [10.1051/mmnp/2025011].
Non-local hyperbolic dynamics of clusters
Garavello M.
2025
Abstract
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.
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Colombo-Garavello-2025-Mathematical Modelling of Natural Phenomena-VoR.pdf
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