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Article
Open AccessA nonlocal Lagrangian traffic flow model and the zero-filter limit
In this study, we start from a Follow-the-Leaders model for traffic flow that is based on a weighted harmonic mean (in Lagrangian coordinates) of the downstream car density. This results in a nonlocal Lagrangi...
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Article
Open AccessOn a singular limit as \(\theta \rightarrow 0\) for a model for the evolution of morphogens in a growing tissue
This paper is devoted to the singular limit of a model for the regulation of growth and patterning in develo** tissues by diffusing morphogens. The model is governed by a system of nonlinear PDEs. The argume...
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Article
Open AccessQualitative Aspects in Nonlocal Dynamics
In this paper, we investigate, through numerical studies, the dynamical evolutions encoded in a linear one-dimensional nonlocal equation arising in peridynamics. The different propagation regimes ranging from ...
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Article
On a model for the evolution of morphogens in a growing tissue II: \(\varvec{\theta = \log (2)}\) case
We analyze a model for the regulation of growth and patterning in develo** tissues by diffusing morphogens. We prove the well-posedness of the underlying systems of nonlinear PDEs. The key tool in the analys...