89 citations · 135 across the 11 of their papers we have counts for
15 papers
Discrete Sobolev and Trudinger inequalities on polyhedral meshes
Maxime Herda, Ariane Trescases, Antoine Zurek
We revisit the derivation of discrete Sobolev and related inequalities on bounded domains for piecewise constant functions on polyhedral meshes. Our results improve the dependence…
A finite volume scheme for the local sensing chemotaxis model
Maxime Herda, Ariane Trescases, Antoine Zurek
In this paper we design, analyze and simulate a finite volume scheme for a cross-diffusion system which models chemotaxis with local sensing. This system has the same Lyapunov func…
No pattern formation in a quasilinear chemotaxis model with local sensing
Philippe Laurençot, Ariane Trescases
Convergence to spatially homogeneous steady states is shown for a chemotaxis model with local sensing and possibly nonlinear diffusion when the intrinsic diffusion rate dominat…
Hyperbolicity and non-conservativity of a hydrodynamic model of swarming rigid bodies
Pierre Degond, Amic Frouvelle, Sara Merino-Aceituno +1
In this paper, we study a nonlinear system of first order partial differential equations describing the macroscopic behavior of an ensemble of interacting self-propelled rigid bodi…
Multi-species viscous models for tissue growth: incompressible limit and qualitative behaviour
Pierre Degond, Sophie Hecht, Michèle Romanos +1
We introduce two 2D mechanical models reproducing the evolution of two viscous tissues in contact. Their main property is to model the swirling cell motions while keeping the tissu…
Global smooth solutions for triangular reaction-cross diffusion systems
Jessica Guerand, Angeliki Menegaki, Ariane Trescases
For a class of reaction cross-diffusion systems of two equations with a cross-diffusion term in the first equation and with self-diffusion terms, we prove that the unique local smo…
Weak solutions to triangular cross diffusion systems modeling chemotaxis with local sensing
Laurent Desvillettes, Philippe Laurençot, Ariane Trescases +1
New estimates and global existence results are provided for a class of systems of cross diffusion equations arising from the modeling of chemotaxis with local sensing, possibly fea…
Delayed Blow-Up for Chemotaxis Models with Local Sensing
Martin Burger, Philippe Laurençot, Ariane Trescases
The aim of this paper is to analyze a model for chemotaxis based on a local sensing mechanism instead of the gradient sensing mechanism used in the celebrated minimal Keller-Segel…
Alignment of self-propelled rigid bodies: from particle systems to macroscopic equations
Pierre Degond, Amic Frouvelle, Sara Merino-Aceituno +1
The goal of these lecture notes is to present in a unified way various models for the dynamics of aligning self-propelled rigid bodies at different scales and the links between the…
Quaternions in collective dynamics
Pierre Degond, Amic Frouvelle, Sara Merino-Aceituno +1
We introduce a model of multi-agent dynamics for self-organised motion; individuals travel at a constant speed while trying to adopt the averaged body attitude of their neighbours.…
On triangular reaction cross-diffusion systems with possible self-diffusion
Ariane Trescases
We present new results of existence of global solutions for a class of reaction cross-diffusion systems of two equations presenting a cross-diffusion term in the first equation, an…
On the entropic structure of reaction-cross diffusion systems
Laurent Desvillettes, Thomas Lepoutre, Ayman Moussa +1
This paper is devoted to the study of systems of reaction-cross diffusion equations arising in population dynamics. New results of existence of weak solutions are presented, allowi…
BV-regularity of the Boltzmann equation in Non-Convex Domains
Yan Guo, Chanwoo Kim, Daniela Tonon +1
Consider the Boltzmann equation in a general non-convex domain with the diffuse boundary condition. We establish optimal BV estimates for such solutions. Our method consists of a n…
New results for triangular reaction cross diffusion system
Laurent Desvillettes, Ariane Trescases
We present an approach based on entropy and duality methods for triangular reaction cross diffusion systems of two equations, in which cross diffusion terms appear only in one of t…
Regularity of the Boltzmann Equation in Convex Domains
Yan Guo, Chanwoo Kim, Daniela Tonon +1
A basic question about regularity of Boltzmann solutions in the presence of physical boundary conditions has been open due to characteristic nature of the boundary as well as the n…