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In this contribution, we study scalar nonlocal conservation laws with the $p$-norm. Here, 'nonlocal' means that the velocity of the conservation law depends on an integral term in space. Typically, the nonlocal term consists of integrating…
In this article, we present a method to find a solution to a one-dimensional nonlocal conservation law that respects a space-dependent mapping, referred to as the obstacle. This is achieved by generalizing existing results for the local…
We introduce the notion of entropy solutions (e.s.) to a conservation law with an arbitrary jump continuous flux vector and prove existence of the largest and the smallest e.s. to the Cauchy problem. The monotonicity and stability…
We consider a class of nonlocal conservation laws with exponential kernel and prove that quantities involving the nonlocal term $W:=\mathbb{1}_{(-\infty,0]}(\cdot)\exp(\cdot) \ast \rho$ satisfy an Ole\u{\i}nik-type entropy condition. More…
We consider solutions of the Aw-Rascle model for traffic flow fulfilling a constraint on the flux at $x=0$. Two different kinds of solutions are proposed: at $x=0$ the first one conserves both the number of vehicles and the generalized…
We discuss a nonlocal version of the Generalized Aw-Rascle-Zhang model, a second-order vehicular traffic model where the empty road velocity is a Lagrangian marker governed by a transport equation. The evolution of the car density is…
We prove the stability of entropy solutions of nonlinear conservation laws with respect to perturbations of the initial datum, the space-time dependent flux and the entropy inequalities. Such a general stability theorem is motivated by the…
The aim of this article is to study the limiting behavior of the solutions for the scaled generalized Euler equations of compressible fluid flow. When the initial data is of Riemann type, we showed the existence of solution which consists…
We found the precise condition for the decay as $t\to\infty$ of Besicovitch almost periodic entropy solutions of multidimensional scalar conservation laws. Moreover, in the case of one space variable we establish asymptotic convergence of…
We present a new class of macroscopic models for pedestrian flows. Each individual is assumed to move towards a fixed target, deviating from the best path according to the instantaneous crowd distribution. The resulting equation is a…
This paper considers numerical discretization of a nonlocal conservation law modeling vehicular traffic flows involving nonlocal inter-vehicle interactions. The nonlocal model involves an integral over the range measured by a horizon…
Inthispaper,weintroduceanon-localPDE-ODEtrafficmodeldevotedtothedescriptionof a 1-to-1 junction with buffer. We present an existence result in the free flow case as well as a numerical method to approximate weak solutions in the general…
In this paper, we present a class of systems of non-local conservation laws in one space-dimension incorporating time delay, which can be used to investigate the interaction between autonomous and human-driven vehicles, each characterized…
We are concerned with spherically symmetric solutions to the Euler equations for the multi-dimensional compressible fluids, which have many applications in diverse real physical situations. The system can be reduced to one dimensional…
This article deals with the error estimates for numerical approximations of the entropy solutions of coupled systems of nonlocal hyperbolic conservation laws. The systems can be strongly coupled through the nonlocal coefficient present in…
In this work we present a rather general approach to approximate the solutions of nonlocal conservation laws. In a first step, we approximate the nonlocal term with an appropriate quadrature rule applied to the spatial discretization. Then,…
We are concerned with the global existence of finite-energy entropy solutions of the one-dimensional compressible Euler equations with (possibly) damping, alignment forces, and nonlocal interactions: Newtonian repulsion and quadratic…
In this paper we study a model for traffic flow on networks based on a hyperbolic system of conservation laws with discontinuous flux. Each equation describes the density evolution of vehicles having a common path along the network. In this…
We consider nonlocal curvature functionals associated with positive interaction kernels, and we show that local anisotropic mean curvature functionals can be retrieved in a blow-up limit from them. As a consequence, we prove that the…
In this note, we introduce some models of pedestrian traffic and prove existence and uniqueness for these models.