Zobrazeno 1 - 10
of 69
pro vyhledávání: '"Herda, Maxime"'
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 size exclusion yielding cross-diffusion. Our method utilizes a two-po
Externí odkaz:
http://arxiv.org/abs/2411.11583
An instationary drift-diffusion system for the electron, hole, and oxygen vacancy densities, coupled to the Poisson equation for the electric potential, is analyzed in a bounded domain with mixed Dirichlet-Neumann boundary conditions. The electron an
Externí odkaz:
http://arxiv.org/abs/2409.01196
Autor:
Gervais, Pierre, Herda, Maxime
We study the well-posedness, steady states and long time behavior of solutions to Vlasov-Fokker-Planck equation with external confinement potential and nonlinear self-consistent interactions. Our analysis introduces newly characterized conditions on
Externí odkaz:
http://arxiv.org/abs/2408.16468
Publikováno v:
Comptes Rendus. Mathématique, Vol 358, Iss 3, Pp 333-340 (2020)
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–Planck equation, for which we adapt hypocoercivity techniques in or
Externí odkaz:
https://doaj.org/article/0951be32f8ac495d9e1ea1bbdad56a5d
Autor:
Cesbron, Ludovic, Herda, Maxime
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 accelerator. We show existence and uniqueness of global classical sol
Externí odkaz:
http://arxiv.org/abs/2307.15964
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 a simplified toy model. From a mathematical perspective, this amounts
Externí odkaz:
http://arxiv.org/abs/2307.13362
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 nonlinearly (e.g. due to Fermi-Dirac statistics). To incorporate volume exclus
Externí odkaz:
http://arxiv.org/abs/2209.07934
Autor:
Herda, Maxime, Zurek, Antoine
Publikováno v:
ESAIM: M2AN, volume 57, 2023, 1589 - 1617
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 scheme, derive qualitative properties of the solutions and prove its co
Externí odkaz:
http://arxiv.org/abs/2207.01928
Autor:
Cesbron, Ludovic, Herda, Maxime
Publikováno v:
In Journal of Differential Equations 25 September 2024 404:316-353
In this paper, we introduce and analyse numerical schemes for the homogeneous and the kinetic L\'evy-Fokker-Planck equation. The discretizations are designed to preserve the main features of the continuous model such as conservation of mass, heavy-ta
Externí odkaz:
http://arxiv.org/abs/2107.13416