1,720,986 research outputs found
Uniqueness and Stability of Solutions for Temple Class Systems with Boundary and Properties of the Attainable Sets
No full textSummary:
The authors consider the initial-boundary value problem for a strictly hyperbolic, genuinely nonlinear, Temple class system of conservation laws on the quarter t-x plane
where . For a class of initial and boundary data in with possibly unbounded variation, they construct a flow of solutions that depend continuously, in the distance, both on the initial data and on the boundary data. Moreover, we show that each trajectory of such flow provides the unique weak solution of the corresponding initial-boundary value problem that satisfies an entropy condition of Oleinik type.
Next, they study the initial-boundary value problem from the point of view of control theory, taking the initial data fixed and considering, in connection with a prescribed set of boundary data regarded as admissible controls, the set of attainable profiles at a fixed time and at a fixed point ,
establishing closure and compactness of such sets in the topolog..
Existence results for Hughes' model for pedestrian flows
No full textIn this paper we prove two global existence results for Hughes' model for pedestrian flows under assumptions that ensure that the traces of the solutions along the turning curve are zero for any positive times
A Hyperbolic–parabolic framework to manage traffic generated pollution
No full textVehicular traffic flows through a merge regulated by traffic lights and produces pollutant that diffuses in the surrounding region. This situation motivates a general hyperbolic- parabolic system, whose well-posedness and stability are here proved in L-1. Roads are allowed to be also 2-dimensional. The effects of stop & go waves are comprised, leading to measure source terms in the parabolic equation. The traffic lights, as well as inflows and outflows, can be regulated to minimize the presence of pollutant in given regions
High-order Finite Volume WENO schemes for non-local multi-class traffic flow models
No full textThis paper focuses on the numerical approximation of a class of non-local systems of conservation laws in one space dimension, arising in traffic modeling, proposed by [F. A. Chiarello and P. Goatin. Non-local multi-class traffic flow models. Networks and Heteroge-neous Media, to appear, Aug. 2018]. We present the multi-class version of the Finite Volume WENO (FV-WENO) schemes [C. Chalons, P. Goatin, and L. M. Villada. High-order numerical schemes for one-dimensional non-local conservation laws. SIAM Journal on Scientific Computing, 40(1):A288–A305, 2018.], with quadratic polynomial reconstruction in each cell to evaluate the non-local terms in order to obtain high-order of accuracy. Simulations using FV-WENO schemes for a multi-class model for autonomous
and human-driven traffic flow are presented for M =
Interacting moving bottlenecks in traffic flow
No full textWe present a general multi-scale approach for modeling the interaction of controlled autonomous vehicles (AVs) with the surrounding traffic flow. The model consists of a scalar conservation law for the bulk traffic, coupled with ordinary differential equations describing the possibly interacting AV trajectories. The coupling is realized through flux constraints at the moving bottleneck positions, inducing the formation of non-classical jump discontinuities in the traffic density. In turn, AVs are forced to adapt their speed to the downstream traffic average velocity in congested situations. We analyze the model solutions in a Riemann-type setting, and propose an adapted finite volume scheme to compute approximate solutions for general initial data. The work paves the way to the study of general optimal control strategies for AV velocities, aiming at improving the overall traffic flow by reducing congestion phenomena and the associated externalities
Lagrangian-antidiffusive remap schemes for non-local multi-class traffic flow models
Full text linkThis paper focuses on the numerical approximation of the solutions of a class of non-local systems in one space dimension, arising in traffic modeling. We propose alternative simple schemes by splitting the non-local conservation laws into two different equations, namely the Lagrangian and the remap steps. We provide some properties and estimates recovered by approximating the problem with the Lagrangian-antidiffusive remap (L-AR) scheme, and we prove the convergence to weak solutions in the scalar case. Finally, we show some numerical simulations illustrating the efficiency of the L-AR schemes in comparison with classical first- and second-order numerical schemes
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