Related papers: General Stability Estimates in NonLocal Traffic Mo…
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 the regularity of the velocity) to the entropy solution of the…
The Gipps car-following model is a widely used tool for studying and simulation traffic dynamics. Despite its popularity an often disregarded property is that under heterogeneous parametrization on the individual vehicles in the traffic…
We investigate the behavior of extended urban traffic networks within the framework of percolation theory by using real and synthetic traffic data. Our main focus shifts from the statistical properties of the cluster size distribution…
We prove existence and boundedness of classical solutions for a family of viscous conservation laws in one space dimension for arbitrarily large time. The result relies on H. Amann's criterion for global existence of solutions and on…
Flocculation is the process whereby particles (i.e., flocs) in suspension reversibly combine and separate. The process is widespread in soft matter and aerosol physics as well as environmental science and engineering. We consider a general…
We prove a concise and easily verifiable criterion on the existence and global stability of stationary solutions for random dynamical systems (RDSs). As a consequence, we can show that the $\omega$-limit sets of all pullback trajectories of…
We prove the stability with respect to the flux of solutions to initial-boundary value problems for scalar non-autonomous conservation laws in one space dimension. Key estimates are obtained through a careful construction of the solutions.
Reduced order models of nonlinear conservation laws in fluid dynamics do not typically inherit stability properties of the full order model. We introduce projection-based hyper-reduced models of nonlinear conservation laws which are…
We show that a class of nonlocal gravity models, proposed to explain current cosmic acceleration without dark energy, passes two major tests: First, they can be defined so as not to alter the, observationally correct, general relativity…
Robustness guarantees are important properties to be looked for during control design. They ensure stability of closed-loop systems in face of uncertainties, unmodeled effects and bounded disturbances. While the theory on robust stability…
This article is concerned with the study of weak solutions of a linear transport equation on a bounded domain with coupled boundary data for general non smooth space and time dependent velocity fields. The existence of solutions, its…
We study ergodic properties of a family of traffic maps acting in the space of bi-infinite sequences of real numbers. The corresponding dynamics mimics the motion of vehicles in a simple traffic flow, which explains the name. Using…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
Stability theory plays a crucial role in feedback control. However, adaptive control theory requires advanced and specialized stability notions that are not frequently used in standard feedback control theory. The present document is a set…
This paper deals with the finite-time stabilization of a class of nonlinear infinite-dimensional systems. First, we consider a bounded matched perturbation in its linear form. It is shown that by using a set-valued function, both the…
We study a 1D scalar conservation law whose non-local flux has a single spatial discontinuity. This model is intended to describe traffic flow on a road with rough conditions. We approximate the problem through an upwind-type numerical…
We prove large-data local stability theorems for several spin models in two dimensions.
A combination of implicit and explicit timestepping is analyzed for a system of ODEs motivated by ones arising from spatial discretizations of evolutionary partial differential equations. Loosely speaking, the method we consider is implicit…
The first part of this paper contains a brief introduction to conservation law models of traffic flow on a network of roads. Globally optimal solutions and Nash equilibrium solutions are reviewed, with several groups of drivers sharing…
Global existence is established for classical solutions to a chemotaxis model with signal-dependent motility for a general class of motility functions $\gamma$ which may in particular decay in an arbitrary way at infinity. Assuming further…