This paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider single conservation law, deduced from the of number cars, defined on road network that collection roads junctions. The evolution problem underdetermined at junctions; hence choose to have some fixed rules distribution plus optimization criteria flux. We prove existence solutions Cauchy and show Lipschitz continuous dependence by initial data does not hold in general, but it under special...

The article deals with a fluid dynamic model for traffic flow on road network. This consists of hyperbolic system two equations proposed in Aw and Rascle (2000 , A. M. ( 2000 ). Resurrection "second order" models . SIAM J. Appl. Math. 60 3 ): 916 – 938 [CSA] [Crossref], [Web Science ®] [Google Scholar]). A method to solve Riemann problems at junctions is given assigning rules distributions maximizations fluxes other quantities. Then we discuss stability L ∞ norm such solutions. Finally,...

We present a new class of macroscopic models for pedestrian flows. Each individual is assumed to move towards fixed target, deviating from the best path according instantaneous crowd distribution. The resulting equation conservation law with nonlocal flux. in this generates Lipschitz semigroup solutions and stable respect functions parameters defining it. Moreover, key qualitative properties such as boundedness density are proved. Specific presented their shown through numerical...

The broad research thematic of flows on networks was addressed in recent years by many researchers, the area applied mathematics, with new models based partial differential equations. latter brought a significant innovation field previously dominated more classical techniques from discrete mathematics or methods ordinary In particular, number results, mainly dealing vehicular traffic, supply chains and data networks, were collected two monographs: Traffic flow , AIMSciences, Springfield,...

We consider a hybrid control system and general optimal problems for this system. suppose that the switching strategy imposes restrictions on sets we provide necessary conditions an trajectory, stating principle (HNP). Our result generalizes various principles available in literature.

We consider a hyperbolic conservation law with discontinuous flux. Such partial differential equation arises in different applications, particular we are motivated by model of traffic flow. provide new formulation terms Riemann Solvers. Moreover, determine the class Solvers which existence and uniqueness corresponding weak entropic solutions.

This work is devoted to the solution Riemann Problems for $p$-system at a junction, main goal being extension case of an ideal junction classical results that hold in standard case.

We present a model for the description of nonviscous isentropic or isothermal fluid crossing junction. Aiming at an extension usual Euler equations, we neglect effects friction against walls pipes, but reaction constraints junction are considered. The well posedness Cauchy problem is proved, and some qualitative properties described.

Abstract We present an epidemic model capable of describing key features the Covid-19 pandemic. While capturing several qualitative properties virus spreading, it allows to compute basic reproduction number, number deaths due and various other statistics. Numerical integrations are used illustrate adherence evolutions described by specific well known real In particular, this is consistent with relevance quarantine, shows dramatic role care houses accounts for increase in death toll when...

Motivated by applications to the piston problem, a manhole model, blood flow and supply chain dynamics, this paper deals with system of conservation laws coupled ordinary differential equations. The former is defined on domain boundary coupling provided condition. For each examples considered, numerical integrations are provided.

We consider the Lighthill-Whitham-Richards traffic flow model on a network composed by an arbitrary number of incoming and outgoing arcs connected together node with buffer. Similar to [15], we define solution Riemann problem at prove existence well posedness solutions Cauchy problem, using wave-front tracking technique generalized tangent vectors.

The paper is concerned with the optimal harvesting of a marine park, which described by parabolic heat equation Neumann boundary conditions and nonlinear source term. We consider cost functional, linear respect to control; hence solution can belong class measure-valued control strategies. For each function, we prove existence stability estimates for solutions equation. Moreover, an solution. Finally, some numerical simulations conclude paper.

We prove global existence, uniqueness and $\L1$ stability of solutions to general systems nonlocal conservation laws modeling multiclass vehicular traffic. Each class follows its own speed law has specific effects on the other classes' speeds. Moreover, explicit dependencies space time are allowed. Solutions proved depend continuously -- in suitable norms all terms appearing equations, as well initial data. Numerical simulations show relevance terms.

The formation, movement and gluing of clusters can be described through a system non-local conservation laws. Here, the well-posedness this is obtained, as well various stability estimates. Remarkably, qualitative properties solutions are proved, providing information on stationary propagation speed. In some cases, fragmentation leads to developing independently. Moreover, these equations may serve an encryption/decryption tool. This poses new analytical problems asks for improved numerical methods.

We construct a model of traffic flow with sources and destinations on roads network.The is based conservation law for the density semilinear equations traffic-type functions, i.e. functions describing paths cars.We propose definition solution at junctions, which depends functions.Finally we prove, every positive time T , existence entropic solutions whole network perturbations constant initial data.Our method wave-front tracking approach.

We consider the vanishing viscosity approximation of traffic model, proposed by Lighthill, Whitham, and Richards, on a network composed single junction with n incoming m outgoing roads. prove that solution parabolic exists and, as vanishes, problem converges to original problem.