62 citations · 117 across the 28 of their papers we have counts for
33 papers
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…
Mathematical derivation of wave propagation properties in hierarchical neural networks with predictive coding feedback dynamics
Grégory Faye, Guilhem Fouilhé, Rufin VanRullen
Sensory perception (e.g. vision) relies on a hierarchy of cortical areas, in which neural activity propagates in both directions, to convey information not only about sensory input…
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…
Generalized gaussian bounds for discrete convolution powers
Jean-François Coulombel, Grégory Faye
We prove a uniform generalized gaussian bound for the powers of a discrete convolution operator in one space dimension. Our bound is derived under the assumption that the Fourier t…
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…
Corrigendum to "Center Manifolds without a Phase Space"
Gregory Faye, Arnd Scheel
We correct the choice of cut-off function in our construction of center manifolds in [G. Faye and A. Scheel, \textit{Trans. Amer. Math. Soc.}, 370 (2018), pp. 5843--5885]. The main…
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…
Threshold of front propagation in neural fields: An interface dynamics approach
Gregory Faye, Zachary P Kilpatrick
Neural field equations model population dynamics of large-scale networks of neurons. Wave propagation in neural fields is often studied by constructing traveling wave solutions in…
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…
Bifurcation to locked fronts in two component reaction-diffusion systems
Gregory Faye, Matt Holzer
We study invasion fronts and spreading speeds in two component reaction-diffusion systems. Using a variation of Lin's method, we construct traveling front solutions and show the ex…
Center manifolds without a phase space
Gregory Faye, Arnd Scheel
We establish center manifold theorems that allow one to study the bifurcation of small solutions from a trivial state in systems of functional equations posed on the real line. The…
Linear spreading speeds from nonlinear resonant interaction
Gregory Faye, Matt Holzer, Arnd Scheel
We identify a new mechanism for propagation into unstable states in spatially extended systems, that is based on resonant interaction in the leading edge of invasion fronts. Such r…
Pinning and Unpinning in Nonlocal Systems
Taylor Anderson, Gregory Faye, Arnd Scheel +1
We investigate pinning regions and unpinning asymptotics in nonlocal equations. We show that phenomena are related to but different from pinning in discrete and inhomogeneous media…