204 research outputs found
Analysis of a chemotaxis system modeling ant foraging
In this paper we analyze a system of PDEs recently introduced in [P. Amorim,
{\it Modeling ant foraging: a {chemotaxis} approach with pheromones and trail
formation}], in order to describe the dynamics of ant foraging. The system is
made of convection-diffusion-reaction equations, and the coupling is driven by
chemotaxis mechanisms. We establish the well-posedness for the model, and
investigate the regularity issue for a large class of integrable data. Our main
focus is on the (physically relevant) two-dimensional case with boundary
conditions, where we prove that the solutions remain bounded for all times. The
proof involves a series of fine \emph{a priori} estimates in Lebesgue spaces.Comment: 39 page
Low Field Regime for the Relativistic Vlasov-Maxwell-Fokker-Planck System; the One and One Half Dimensional Case
International audienceWe study the asymptotic regime for the relativistic Vlasov-Maxwell-Fokker-Planck system which corresponds to a mean free path small compared to the Debye length, chosen as an observation length scale, combined to a large thermal velocity assumption. We are led to a convection-diffusion equation, where the convection velocity is obtained by solving a Poisson equation. The analysis is performed in the one and one half dimensional case and the proof combines dissipation mechanisms and finite speed of propagation properties
From Vlasov-Poisson and Vlasov-Poisson-Fokker-Planck Systems to Incompressible Euler Equations: the case with finite charge
We study the asymptotic regime of strong electric fields that leads from the
Vlasov-Poisson system to the Incompressible Euler equations. We also deal with
the Vlasov-Poisson-Fokker-Planck system which induces dissipative effects. The
originality consists in considering a situation with a finite total charge
confined by a strong external field. In turn, the limiting equation is set in a
bounded domain, the shape of which is determined by the external confining
potential. The analysis extends to the situation where the limiting density is
non-homogeneous and where the Euler equation is replaced by the Lake Equation,
also called Anelastic Equation.Comment: 39 pages, 3 figure
A Numerical Study on Large-Time Asymptotics of the Lifshitz-Slyozov System
We numerically investigate the behaviour for long time of solutions of the Lifshitz-Slyozov system. In particular, we find this behaviour to crucially depend on the distribution of largest aggregates present in the solution
Discrete Version of the She Asymptotics: Multigroup Neutron Transport Equations
This paper is devoted to the derivation of multigroup diffusion equations from the Boltzmann equation. The limit system couples the energy levels from both zeroth order term and diffusion currents
A simple testbed for stability analysis of quantum dissipative systems
We study a two-state quantum system with a non linearity intended to describe
interactions with a complex environment, arising through a non local coupling
term. We study the stability of particular solutions, obtained as constrained
extrema of the energy functional of the system. The simplicity of the model
allows us to justify a complete stability analysis. This is the opportunity to
review in details the techniques to investigate the stability issue. We also
bring out the limitations of perturbative approaches based on simpler
asymptotic models
Plane wave stability analysis of Hartree and quantum dissipative systems
We investigate the stability of plane wave solutions of equations describing
quantum particles interacting with a complex environment. The models take the
form of PDE systems with a non local (in space or in space and time)
self-consistent potential; such a coupling lead to challenging issues compared
to the usual non linear Schr{\"o}dinger equations. The analysis relies on the
identification of suitable Hamiltonian structures and Lyapounov functionals. We
point out analogies and differences between the original model, involving a
coupling with a wave equation, and its asymptotic counterpart obtained in the
large wave speed regime. In particular, while the analogies provide interesting
intuitions, our analysis shows that it is illusory to obtain results on the
former based on a perturbative analysis from the latter
Vanishing pressure in gas dynamics equations
International audienceThe smooth solutions of gas dynamics system as the pressure goes to 0 converge toward a solution of the pressureless gas model
- …