Mercoledì 1° Aprile 2026 alle ore 16:45, nel quadro del ciclo di seminari Matematica in Azione, Davide Meroni (Università degli Studi di Milano-Bicocca) e Andrea Salvadori (Università degli Studi dell’Aquila e University of Tours) terranno i seguenti interventi
Relatore: Davide Meroni
Titolo: ARZ-type model of vehicular traffic with local constrained flow
Abstract: The Aw-Rascle-Zhang traffic model is a 2 × 2 system of conservation laws developed to provide a more accurate representation of traffic flow. In particular, we are interested in the evolution of cars’ density subjected to a local constraint representing the presence of a traffic light. In this talk, we begin with a brief introduction to the theory of systems of conservation laws. We then introduce the ARZ model and study the associated Riemann problem, namely the Cauchy problem with initial data consisting of two constant states separated by a single jump discontinuity. Then, we turn to the constrained Riemann problem and analyze its solutions. Finally, we describe some results and open questions for the Cauchy problem when the classical ARZ flux is replaced by a more general function, which encompasses a broader class of models.
Relatore: Andrea Salvadori
Titolo: General Non Local Balance Laws: from Clustering to Cryptography
Abstract: In recent years, the analytical theory of non local balance laws has been widely explored, fueled by a variety of applications, most commonly involving supply chains and traffic flow models in the one-dimensional case, and population dynamics in the multi-dimensional case. This talk addresses a system of multi-dimensional non local balance laws both from an analytical and an applied perspective. Theoretical results, including well-posedness, L1, L∞, and BV growth estimates, as well as stability estimates with respect to the velocity, the convolution kernel and the source are rigorously established. Interestingly, in contrast to the local setting, the solution exhibits time reversibility, implying that for an autonomous system, the usual semigroup generated by balance laws is, in fact, a group. In the general case, when the equation explicitly depends on time, we show that it generates a reversible process, which enjoys analogous properties. From a modeling perspective, this class of equations naturally captures clustering phenomena, such as gluing, movement, and fragmentation, making it suitable for describing population dynamics. As an example, we introduce a predator-prey model illustrating these dynamics. The time reversibility also opens the door to novel applications in cryptography. We propose a symmetric cipher, where the private key is defined by the parameters entering in the equation, and numerically investigate its behavior by encrypting text messages and images; the results are presented and compared. Furthermore, we suggest a quantitative approach to evaluate the quality of this cryptosystem beyond simple visual inspection. This innovative application of balance laws yields new analytical and numerical open problems of theoretical interest, explored from a non-standard perspective. Work in collaboration with D. Amadori (University of L’Aquila) and R.M. Colombo (University of Brescia).
Informazioni per partecipare
Il seminario si terrà in Aula U1-02 (Edificio U1 | Piazza della Scienza 1, Milano).
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