arXiv subjects

Massimiliano Daniele Rosini

Publications and source records attributed to Massimiliano Daniele Rosini.

4 recordsLinked to original sources

arXiv2026

On a $2x2$ system of conservation laws with discontinuous flux

We study a one-dimensional $2x2$ system of conservation laws with discontinuous flux. We prove the global existence of weak solutions for initial data with sufficiently small total variation. We construct explicitly the associated Riemann solver and analyze its main properties. Finally, we introduce a Glimm-type numerical scheme tailored to the exact Riemann solver and use it to reproduce the wave patterns obtained analytically.

math.AP↗

arXiv2026

Existence result for a 2 x 2 system of conservation laws with discontinuous flux and applications

This paper is concerned with one-dimensional 2 x 2 systems of conservation laws with a flux f=f(x, U) that is discontinuous with respect to the spatial variable. No monotonicity assumption is imposed on the mapping x \to f(x,U). We introduce a Kruzhkov-type entropy condition and establish the global existence of entropy solutions for large data. The proof relies on a wave-front tracking approximation. The main technical novelty consists in the introduction of adapted Riemann invariant coordinates, specifically designed to account for the discontinuities of the flux, which yield a uniform-in-time bound on the total variation of the approximate solutions U^n(t). We also outline several alternative approaches that may lead to existence results under possibly weaker assumptions. As an application, we propose second-order vehicular traffic models on inhomogeneous roads featuring abrupt ''collective'' changes in the speed law or road capacity.

math.AP↗

arXiv2016

Entropy solutions for a traffic model with phase transitions

In this paper, we consider the two phases macroscopic traffic model introduced in [P. Goatin, The Aw-Rascle vehicular traffic flow with phase transitions, Mathematical and Computer Modeling 44 (2006) 287-303]. We first apply the wave-front tracking method to prove existence and a priori bounds for weak solutions. Then, in the case the characteristic field corresponding to the free phase is linearly degenerate, we prove that the obtained weak solutions are in fact entropy solutions à la Kruzhkov. The case of solutions attaining values at the vacuum is considered. We also present an explicit numerical example to describe some qualitative features of the solutions.

math.NA↗

arXiv2015

Qualitative behaviour and numerical approximation of solutions to conservation laws with non-local point constraints on the flux and modeling of crowd dynamics at the bottlenecks

In this paper we investigate numerically the model for pedestrian traffic proposed in [B.Andreianov, C.Donadello, M.D.Rosini, Crowd dynamics and conservation laws with nonlocal constraints and capacity drop, Mathematical Models and Methods in Applied Sciences 24 (13) (2014) 2685-2722]. We prove the convergence of a scheme based on a constraint finite volume method and validate it with an explicit solution obtained in the above reference. We then perform ad hoc simulations to qualitatively validate the model under consideration by proving its ability to reproduce typical phenomena at the bottlenecks, such as Faster Is Slower effect and the Braess' paradox.

math.NA↗