44 citations · 135 across the 29 of their papers we have counts for
23 papers · 1 filter
Entropy and Fisher information in non-convex domains: one chain to rule them all
Jean-Baptiste Casteras, Marco Flaim, Léonard Monsaingeon
We prove that the (square root) Fisher information functional is a strong Wasserstein upper gradient of the entropy on non-convex Riemannian domains. This fills a gap in the litera…
A gradient flow that is none: Heat flow with Wentzell boundary condition
Marie Bormann, Léonard Monsaingeon, D. R. Michiel Renger +1
We establish a representation of the heat flow with Wentzell boundary conditions on smooth domains as gradient descent dynamics for the entropy in a suitably extended Otto manifold…
Large deviations for sticky-reflecting Brownian motion with boundary diffusion
Jean-Baptiste Casteras, Leonard Monsaingeon, Luca Nenna
We study a Schilder-type large deviation principle for sticky-reflected Brownian motion with boundary diffusion, both at the static and sample path level in the short-time limit. A…
Discretizing the Fokker-Planck equation with second-order accuracy: a dissipation driven approach
Clément Cancès, Léonard Monsaingeon, Andrea Natale
We propose a fully discrete finite volume scheme for the standard Fokker-Planck equation. The space discretization relies on the well-known square-root approximation, which falls i…
Sticky-reflecting diffusion as a Wasserstein gradient flow
Jean-Baptiste Casteras, Léonard Monsaingeon, Filippo Santambrogio
In this paper we identify the Fokker-Planck equation for (reflected) Sticky Brownian Motion as a Wasserstein gradient flow in the space of probability measures. The driving functio…
Construction of 2-bubbles for the energy critical bi-harmonic Schrödinger equation
Jean-Baptiste Casteras, Ilkka Holopainen, Léonard Monsaingeon
We construct a blowing-up solution for the energy critical focusing biharmonic nonlinear Schrödinger equation in infinite time in dimension . Our solution is radially sym…
Hidden dissipation and convexity for Kimura equations
Jean-Baptiste Casteras, Léonard Monsaingeon
In this paper we establish a rigorous gradient flow structure for one-dimensional Kimura equations with respect to some Wasserstein-Shahshahani optimal transport geometry. This is…
Invariant measures and global well-posedness for a fractional Schrödinger equation with Moser-Trudinger type nonlinearity
Jean-Baptiste Casteras, Léonard Monsaingeon
In this paper, we construct invariant measures and global-in-time solutions for a fractional Schr\" odinger equation with a Moser-Trudinger type nonlinearity $$ i\partial_t u= (-Δ)…
A degenerate elliptic-parabolic system arising in competitive contaminant transport
Margarida Baía, Farid Bozorgnia, Léonard Monsaingeon +1
In this work we investigate a coupled system of degenerate and nonlinear partial differential equations governing the transport of reactive solutes in groundwater. We show that the…
A new transportation distance with bulk/interface interactions and flux penalization
Léonard Monsaingeon
We introduce and study a new optimal transport problem on a bounded domain , defined via a dynamical Benamou-Brenier formulation. The model handles differ…
Small noise limit and convexity for generalized incompressible flows, Schrödinger problems, and optimal transport
Aymeric Baradat, Léonard Monsaingeon
This paper is concerned with six variational problems and their mutual connections: The quadratic Monge-Kantorovich optimal transport, the Schrödinger problem, Brenier's relaxed mo…
An unbalanced Optimal Transport splitting scheme for general advection-reaction-diffusion problems
Thomas Gallouët, Maxime Laborde, Léonard Monsaingeon
In this paper, we show that unbalanced optimal transport provides a convenient framework to handle reaction and diffusion processes in a unified metric framework. We use a construc…
Incompressible immiscible multiphase flows in porous media: a variational approach
Clément Cancès, Thomas Gallouët, Leonard Monsaingeon
We describe the competitive motion of (N + 1) incompressible immiscible phases within a porous medium as the gradient flow of a singular energy in the space of non-negative measure…
A fitness-driven cross-diffusion system from polulation dynamics as a gradient flow
Stanislav Kondratyev, Léonard Monsaingeon, Dmitry Vorotnikov
We consider a fitness-driven model of dispersal of interacting populations, which was previously studied merely in the case . Based on some optimal transport distance rece…
Numerical investigation of the Free Boundary regularity for a degenerate advection-diffusion problem
Léonard Monsaingeon
We study the free boundary regularity of the traveling wave solutions to a degenerate advection-diffusion problem of Porous Medium type, whose existence was proved in \cite{Monsain…
A JKO splitting scheme for Kantorovich-Fisher-Rao gradient flows
Thomas Gallouët, Léonard Monsaingeon
In this article we set up a splitting variant of the JKO scheme in order to handle gradient flows with respect to the Kantorovich-Fisher-Rao metric, recently introduced and defined…
A new optimal transport distance on the space of finite Radon measures
Stanislav Kondratyev, Léonard Monsaingeon, Dmitry Vorotnikov
We introduce a new optimal transport distance between nonnegative finite Radon measures with possibly different masses. The construction is based on non-conservative continuity equ…
A KPP road-field system with spatially periodic exchange terms
Thomas Giletti, Léonard Monsaingeon, Maolin Zhou
We take interest in a reaction-diffusion system which has been recently proposed [11] as a model for the effect of a road on propagation phenomena arising in epidemiology and ecolo…
The gradient flow structure for incompressible immiscible two-phase flows in porous media
Clément Cancès, Thomas O. Gallouët, Léonard Monsaingeon
We show that the widely used model governing the motion of two incompressible immiscible fluids in a possibly heterogeneous porous medium has a formal gradient flow structure. More…
A Wasserstein gradient flow approach to Poisson-Nernst-Planck equations
David Kinderlehrer, Léonard Monsaingeon, Xiang Xu
The Poisson-Nernst-Planck system of equations used to model ionic transport is interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of probabi…
Systems of partial differential equations in porous medium
Tuomo Kuusi, Léonard Monsaingeon, Juha Videman
We investigate systems of degenerate parabolic equations idealizing reactive solute transport in porous media. Taking advantage of the inherent structure of the system that allows…
An algorithm for one-dimensional Generalized Porous Medium Equations: interface tracking and the hole filling problem
Leonard Monsaingeon
Based on results of E. DiBenedetto and D. Hoff we propose an explicit finite difference scheme for the one dimensional Generalized Porous Medium Equation $\partial_t u=\partial_{xx…
Traveling Wave Solutions of Advection-Diffusion Equations with Nonlinear Diffusion
Léonard Monsaingeon, Alexeï Novikov, Jean-Michel Roquejoffre
We study the existence of particular traveling wave solutions of a nonlinear parabolic degenerate diffusion equation with a shear flow. Under some assumptions we prove that such so…