-
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...
-
Article
Dispersive Effects in Two- and Three-Dimensional Peridynamics
In this paper we study the dispersive properties related to a model of peridynamic evolution, governed by a non local initial value problem, in the cases of two and three spatial dimensions. The features of th...
-
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...
-
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 ...
-
Article
Open AccessWaves in Flexural Beams with Nonlinear Adhesive Interaction
The paper studies the initial boundary value problem related to the dynamic evolution of an elastic beam interacting with a substrate through an elastic-breakable forcing term. This discontinuous interaction i...
-
Article
Long time behavior of a model for the evolution of morphogens in a growing tissue
The long time behavior of a model for the regulation of growth and patterning in develo** tissues by diffusing morphogens is analyzed. Such model is expressed in terms of a system of nonlinear PDEs. The key ...
-
Article
Well-posedness of the Initial Value Problem for the Ostrovsky–Hunter Equation with Spatially Dependent Flux
In this paper we study the Ostrovsky–Hunter equation for the case where the flux function f(x, u) may depend on the spatial variable with certain smoothness. Our main results are that if the flux function is smoo...
-
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...
-
Article
A convergent finite difference scheme for the Ostrovsky-Hunter equation on a bounded domain
We prove the convergence of a finite difference scheme to the unique entropy solution of a general form of the Ostrovsky-Hunter equation on a bounded domain with periodic boundary conditions. The equation mode...
-
Article
Analysis and numerical approximation of Brinkman regularization of two-phase flows in porous media
We consider a system of nonlinear partial differential equations that arises in the modeling of two-phase flows in a porous medium. The phase velocities are modeled using a Brinkman regularization of the class...
-
Chapter and Conference Paper
Some Wellposedness Results for the Ostrovsky–Hunter Equation
The Ostrovsky-Hunter equation provides a model for small-amplitude long waves in a rotating fluid of finite depth. It is a nonlinear evolution equation. In this paper the welposedness of the Cauchy problem and...
-
Article
Analytic Solutions and Singularity Formation for the Peakon b-Family Equations
This paper deals with the well-posedness of the b-family equation in analytic function spaces. Using the Abstract Cauchy-Kowalewski theorem we prove that the b-family equation admits, locally in time, a unique an...
-
Chapter and Conference Paper
Global Weak Solutions for a Shallow Water Equation
