30 citations · 111 across the 17 of their papers we have counts for
19 papers
Convergence and long-time behavior of finite volumes for a generalized Poisson-Nernst-Planck system with cross-diffusion and size exclusion
Clément Cancès, Maxime Herda, Annamaria Massimini
We present a finite volume scheme for modeling the diffusion of charged particles, specifically ions, in constrained geometries using a degenerate Poisson-Nernst-Planck system with…
On a Vlasov-Fokker-Planck equation for stored electron beams
Ludovic Cesbron, Maxime Herda
In this paper we study a self-consistent Vlasov-Fokker-Planck equations which describes the longitudinal dynamics of an electron bunch in the storage ring of a synchrotron particle…
Wasserstein contraction for the stochastic Morris-Lecar neuron model
Maxime Herda, Pierre Monmarché, Benoît Perthame
Neuron models have attracted a lot of attention recently, both in mathematics and neuroscience. We are interested in studying long-time and large-population emerging properties in…
Numerical analysis of a finite volume scheme for charge transport in perovskite solar cells
Dilara Abdel, Claire Chainais-Hillairet, Patricio Farrell +1
In this paper, we consider a drift-diffusion charge transport model for perovskite solar cells, where electrons and holes may diffuse linearly (Boltzmann approximation) or nonlinea…
Study of an entropy dissipating finite volume scheme for a nonlocal cross-diffusion system
Maxime Herda, Antoine Zurek
In this paper we analyse a finite volume scheme for a nonlocal version of the Shigesada-Kawazaki-Teramoto (SKT) cross-diffusion system. We prove the existence of solutions to the s…
On a structure-preserving numerical method for fractional Fokker-Planck equations
Nathalie Ayi, Maxime Herda, Hélène Hivert +1
In this paper, we introduce and analyse numerical schemes for the homogeneous and the kinetic Lévy-Fokker-Planck equation. The discretizations are designed to preserve the main fea…
Long-time behaviour of hybrid finite volume schemes for advection-diffusion equations: linear and nonlinear approaches
Claire Chainais-Hillairet, Maxime Herda, Simon Lemaire +1
We are interested in the long-time behaviour of approximate solutions to heterogeneous and anisotropic linear advection-diffusion equations in the framework of hybrid finite volume…
A Fokker-Planck approach to the study of robustness in gene expression
Pierre Degond, Maxime Herda, Sepideh Mirrahimi
We study several Fokker-Planck equations arising from a stochastic chemical kinetic system modeling a gene regulatory network in biology. The densities solving the Fokker-Planck eq…
bounds for numerical solutions of noncoercive convection-diffusion equations
Claire Chainais-Hillairet, Maxime Herda
In this work, we apply an iterative energy method à la de Giorgi in order to establish bounds for numerical solutions of noncoercive convection-diffusion equations wit…
A note on hypocoercivity for kinetic equations with heavy-tailed equilibrium
Nathalie Ayi, Maxime Herda, Hélène Hivert +1
In this paper we are interested in the large time behavior of linear kinetic equations with heavy-tailed local equilibria. Our main contribution concerns the kinetic Lévy-Fokker-Pl…
Large time behavior of nonlinear finite volume schemes for convection-diffusion equations
Clément Cancès, Claire Chainais-Hillairet, Maxime Herda +1
In this contribution we analyze the large time behavior of a family of nonlinear finite volume schemes for anisotropic convection-diffusion equations set in a bounded bidimensional…
A projection algorithm on the set of polynomials with two bounds
Martin Campos Pinto, Frédérique Charles, Bruno Després +1
The motivation of this work stems from the numerical approximation of bounded functions by polynomials satisfying the same bounds. The present contribution makes use of the recent…
Hypocoercivity and diffusion limit of a finite volume scheme for linear kinetic equations
Marianne Bessemoulin-Chatard, Maxime Herda, Thomas Rey
In this article, we are interested in the asymptotic analysis of a finite volume scheme for one dimensional linear kinetic equations, with either Fokker-Planck or linearized BGK co…
Computation of sum of squares polynomials from data points
Bruno Després, Maxime Herda
We propose an iterative algorithm for the numerical computation of sums of squares of polynomials approximating given data at prescribed interpolation points. The method is based o…
Large-time behavior of a family of finite volume schemes for boundary-driven convection-diffusion equations
Claire Chainais-Hillairet, Maxime Herda
We are interested in the large-time behavior of solutions to finite volume discretizations of convection-diffusion equations or systems endowed with non-homogeneous Dirichlet and N…
Large-time behavior of solutions to Vlasov-Poisson-Fokker-Planck equations: from evanescent collisions to diffusive limit
Maxime Herda, Luis Miguel Rodrigues
The present contribution investigates the dynamics generated by the two-dimensional Vlasov-Poisson-Fokker-Planck equation for charged particles in a steady inhomogeneous background…
Anisotropic Boltzmann-Gibbs dynamics of strongly magnetized Vlasov-Fokker-Planck equations
Maxime Herda, Luis Miguel Rodrigues
We consider various sets of Vlasov-Fokker-Planck equations modeling the dynamics of charged particles in a plasma under the effect of a strong magnetic field. For each of them in a…
A finite volume scheme for boundary-driven convection-diffusion equations with relative entropy structure
Francis Filbet, Maxime Herda
We propose a finite volume scheme for a class of nonlinear parabolic equations endowed with non-homogeneous Dirichlet boundary conditions and which admit relative en-tropy function…
On massless electron limit for a multispecies kinetic system with external magnetic field
Maxime Herda
We consider a three-dimensional kinetic model for a two species plasma consisting of electrons and ions confined by an external nonconstant magnetic field. Then we derive a kinetic…