62 citations · 117 across the 28 of their papers we have counts for
19 papers · 1 filter
Sharp asymptotics for a transport model with a nonlocal condition of the Fisher-KPP type at the boundary
Grégory Faye, Jean-Michel Roquejoffre, Mingmin Zhang
This paper is concerned with the precise asymptotics, as time goes to infinity, of a transport problem in a half plane coupled with a nonlinear nonlocal boundary condition. This sy…
Spreading Properties of a City-Road Reaction-Diffusion Model on One-Dimensional Lattice
Grégory Faye, Jean-Michel Roquejoffre, Min Zhao
We propose and study a new model to describe biological invasions constrained on infinite homogeneous one dimensional metric graphs. Our model consists of an infinite PDE-ODE syste…
Existence and stability of nonmonotone hydraulic shocks for the Saint Venant equations of inclined thin-film flow
Grégory Faye, L. Miguel Rodrigues, Zhao Yang +1
Extending work of Yang-Zumbrun for the hydrodynamically stable case of Froude number F < 2, we categorize completely the existence and convective stability of hydraulic shock profi…
Spreading properties in Kermack-McKendrick models with nonlocal spatial interactions -- A new look
Grégory Faye, Jean-Michel Roquejoffre, Mingmin Zhang
In this paper, we revisit the famous Kermack-McKendrick model with nonlocal spatial interactions by shedding new lights on associated spreading properties and we also prove the exi…
Exponential asymptotic stability of Riemann shocks of hyperbolic systems of balance laws
Grégory Faye, L. Miguel Rodrigues
For strictly entropic Riemann shock solutions of strictly hyperbolic systems of balance laws, we prove that exponential spectral stability implies large-time asymptotic orbital sta…
The logarithmic Bramson correction for Fisher-KPP equations on the lattice
Christophe Besse, Grégory Faye, Jean-Michel Roquejoffre +1
We establish in this paper the logarithmic Bramson correction for Fisher-KPP equations on the lattice . The level sets of solutions with step-like initial conditions ar…
Asymptotic behavior of nonlocal bistable reaction-diffusion equations
Christophe Besse, Alexandre Capel, Grégory Faye +1
In this paper, we study the asymptotic behavior of the solutions of nonlocal bistable reaction-diffusion equations starting from compactly supported initial conditions. Depending o…
Spreading properties for SIR models on homogeneous trees
Christophe Besse, Grégory Faye
We consider an epidemic model of SIR type set on a homogeneous tree and investigate the spreading properties of the epidemic as a function of the degree of the tree, the intrinsic…
Asymptotic spreading for Fisher-KPP reaction-diffusion equations with heterogeneous shifting diffusivity
Grégory Faye, Thomas Giletti, Matt Holzer
We determine the asymptotic spreading speed of the solutions of a Fisher-KPP reaction-diffusion equation, starting from compactly supported initial data, when the diffusion coeffic…
Sharp stability for finite difference approximations of hyperbolic equations with boundary conditions
Jean-François Coulombel, Grégory Faye
In this article, we consider a class of finite rank perturbations of Toeplitz operators that have simple eigenvalues on the unit circle. Under a suitable assumption on the behavior…
Dynamics of epidemic spreading on connected graphs
Christophe Besse, Grégory Faye
We propose a new model that describes the dynamics of epidemic spreading on connected graphs. Our model consists in a PDE-ODE system where at each vertex of the graph we have a sta…
Invasion into remnant instability: a case study of front dynamics
Gregory Faye, Matt Holzer, Arnd Scheel +1
We study the invasion of an unstable state by a propagating front in a peculiar but generic situation where the invasion process exhibits a remnant instability. Here, remnant insta…
Quantitative estimates of the threshold phenomena for propagation in reaction-diffusion equations
Matthieu Alfaro, Arnaud Ducrot, Gregory Faye
We focus on the (sharp) threshold phenomena arising in some reaction-diffusion equations supplemented with some compactly supported initial data. In the so-called ignition and bist…
Asymptotic stability of the critical pulled front in a Lotka-Volterra competition model
Gregory Faye, Matt Holzer
We prove that the critical pulled front of Lotka-Volterra competition systems is nonlinearly asymptotically stable. More precisely, we show that perturbations of the critical front…
Rigorous derivation of the nonlocal reaction-diffusion FitzHugh-Nagumo system
Joachim Crevat, Grégory Faye, Francis Filbet
We introduce a spatially extended transport kinetic FitzHugh-Nagumo model with forced local interactions and prove that its hydrodynamic limit converges towards the classical nonlo…
Asymptotic stability of the critical Fisher-KPP front using pointwise estimates
Gregory Faye, Matt Holzer
We propose a simple alternative proof of a famous result of Gallay regarding the nonlinear asymptotic stability of the critical front of the Fisher-KPP equation which shows that pe…
Modulated traveling fronts for a nonlocal Fisher-KPP equation: a dynamical systems approach
Gregory Faye, Matt Holzer
We consider a nonlocal generalization of the Fisher-KPP equation in one spatial dimension. As a parameter is varied the system undergoes a Turing bifurcation. We study the dynamics…
Existence of pulses in excitable media with nonlocal coupling
Gregory Faye, Arnd Scheel
We prove the existence of fast traveling pulse solutions in excitable media with non-local coupling. Existence results had been known, until now, in the case of local, diffusive co…
Fredholm properties of nonlocal differential operators via spectral flow
Gregory Faye, Arnd Scheel
We establish Fredholm properties for a class of nonlocal differential operators. Using mild convergence and localization conditions on the nonlocal terms, we also show how to compu…