5 citations · 15 across the 17 of their papers we have counts for
18 papers
Systems of nonlocal conservation laws: well-posedness and the singular limit for a nonlocal generalized Aw-Rascle-Zhang model
Debora Amadori, Felisia Angela Chiarello, Gianmarco Cipollone +2
In this paper, we study a system of nonlocal conservation laws motivated by traffic flow: a nonlocal version of the generalized Aw-Rascle-Zhang (GARZ) model. The nonlocality arises…
A general framework for nonlocal traffic flow models on networks
Alexander Keimer, Lukas Pflug, Florian Prohaska
We present a general computational framework for macroscopic nonlocal traffic flow models on networks with multiple commodities. The model combines scalar conservation laws on edge…
The obstacle problem for scalar conservation laws with nonlocal dynamics
Paulo Amorim, Alexander Keimer, Lukas Pflug +1
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…
Nonlocal Approximation Principle for Entropy Solutions of Scalar Conservation Laws
Alexander Keimer, Lukas Pflug
We establish a general nonlocal approximation principle for the entropy solutions of scalar conservation laws on . More precisely, we show that the entropy solution to…
Existence and uniqueness of nonlocal nonlinear conservation laws via fixed-point methods
Xiaoqian Gong, Alexander Keimer, Lorenzo Liverani +1
We investigate the well-posedness of scalar conservation laws whose flux depends on the solution both pointwise and nonlocally through integral averages. Our analysis is based on a…
Nonlocal conservation laws with p-norm, the singular limit problem and applications to traffic flow
Felisia Angela Chiarello, Alexander Keimer, Lukas Pflug
In this contribution, we study scalar nonlocal conservation laws with the -norm. Here, 'nonlocal' means that the velocity of the conservation law depends on an integral term in…
Optimal Control Problems with Nonlocal Conservation Laws: Existence of Optimizers and Singular Limits in Approximations of Local Conservation Laws
Alexander Keimer, Lukas Pflug, Jakob Rodestock
This contribution considers optimal control problems subject to nonlocal conservation laws -- those in which the velocity depends nonlocally (i.e., via a convolution) on the soluti…
The obstacle problem for linear scalar conservation laws with constant velocity
Paulo Amorim, Alexander Keimer, Lukas Pflug +1
In this contribution, we present a novel approach for solving the obstacle problem for (linear) conservation laws. Usually, given a conservation law with an initial datum, the solu…
A note on nonlocal approximations of sign-unrestricted solutions of conservation laws
Alexander Keimer, Lukas Pflug
We study the singular limit problem for nonlocal conservation laws in which the sign of the initial datum is unrestricted and the velocity of the conservation law depends on a nonl…
On the singular limit problem for nonlocal conservation laws: A general approximation result for kernels with fixed support
Alexander Keimer, Lukas Pflug
We prove the convergence of solutions of nonlocal conservation laws to their local entropic counterpart for a fundamentally extended class of nonlocal kernels when these kernels ap…
On the singular limit problem in nonlocal balance laws: Applications to nonlocal lane-changing traffic flow models
Felisia Angela Chiarello, Alexander Keimer
We present a convergence result from nonlocal to local behavior for a system of nonlocal balance laws. The velocity field of the underlying conservation laws is diagonal. In contra…
Ole\uınik-type estimates for nonlocal conservation laws and applications to the nonlocal-to-local limit
Giuseppe Maria Coclite, Maria Colombo, Gianluca Crippa +5
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…
Conservation laws with nonlocality in density and velocity and their applicability in traffic flow modelling
Jan Friedrich, Simone Göttlich, Alexander Keimer +1
In this work we present a nonlocal conservation law with a velocity depending on an integral term over a part of the space. The model class covers already existing models in litera…
On the singular limit problem for a discontinuous nonlocal conservation law
Alexander Keimer, Lukas Pflug
In this contribution we study the singular limit problem of a nonlocal conservation law with a discontinuity in space. The specific choice of the nonlocal kernel involving the spat…
Conservation laws with nonlocal velocity -- the singular limit problem
Jan Friedrich, Simone Göttlich, Alexander Keimer +1
We consider conservation laws with nonlocal velocity and show for nonlocal weights of exponential type that the unique solutions converge in a weak or strong sense (dependent on th…
Discontinuous nonlocal conservation laws and related discontinuous ODEs -- Existence, Uniqueness, Stability and Regularity
Alexander Keimer, Lukas Pflug
We study nonlocal conservation laws with a discontinuous flux function of regularity in the spatial variable and show existence and uniqueness of…
A general result on the approximation of local conservation laws by nonlocal conservation laws: The singular limit problem for exponential kernels
Giuseppe Maria Coclite, Jean-Michel Coron, Nicola De Nitti +2
We deal with the problem of approximating a scalar conservation law by a conservation law with nonlocal flux. As convolution kernel in the nonlocal flux, we consider an exponential…
Integration of Information Patterns in the Modeling and Design of Mobility Management Services
Alexander Keimer, Nicolas Laurent-Brouty, Farhad Farokhi +4
Over the last decade, the rise of the mobile internet and the usage of mobile devices has enabled ubiquitous traffic information. With the increased adoption of specific smartphone…