§undergraduate student.

Preprints


- J.-F. Coulombel and G. Faye
Nonlinear orbital stability of stationary shock profiles for the Lax-Wendroff scheme (PDF)

- G. Faye and M. Zhao
The threshold phenomena for propagation in fractional Laplacian diffusion equations (PDF)

- G. Faye, J.-M. Roquejoffre and M. Zhang
Spreading properties in Kermack - McKendrick models with nonlocal spatial interactions – A new look – (PDF)

Publications


- J-F. Coulombel and G. Faye
The local limit theorem for complex valued sequences: the parabolic case (PDF)
Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1801-1818.

- G. Faye, L.M. Rodrigues, Z. Yang and K. Zumbrun
Existence and stability of nonmonotone hydraulic shocks for the Saint Venant equations of inclined thin-film flow (PDF)
Archive for Rational Mechanics and Analysis, vol 248, no 82 (2024), pp. 1-49.

- G. Faye, G. Fouilhé§ and R. VanRullen
Mathematical derivation of wave propagation properties in hierarchical neural networks with predictive coding feedback dynamics (PDF)
Bulletin of Mathematical Biology, vol 85, no 80 (2023) , pp. 1-75

- G. Faye and L.M. Rodrigues
Exponential asymptotic stability of Riemann shocks of hyperbolic systems of balance laws (PDF)
SIAM J. Math. Anal., Vol. 55, No. 6, (2023) pp. 6425-6456

- C. Besse, G. Faye, J.-M. Roquejoffre and M. Zhang
The logarithmic Bramson correction for Fisher-KPP equations on the lattice Z (PDF)
Trans. Amer. Math. Soc. 376 (2023), pp. 8553-8619

- C. Besse, A. Capel§, G. Faye and G. Fouilhé§
Asymptotic behavior of nonlocal bistable reaction-diffusion equations (PDF)
Discrete and Continuous Dynamical Systems Series B, vol 28, issue 12 (2023) , pp. 5967-5997

- J-F. Coulombel and G. Faye
Generalized Gaussian bounds for discrete convolution powers (PDF)
Revista Matematica Iberoamericana, 38 (5) (2022) , pp. 1553-1604

- J-F. Coulombel and G. Faye
Sharp stability for finite difference approximations of hyperbolic equations with boundary conditions (PDF)
IMA Journal of Numerical Analysis, vol 43, Issue 1 (2023) , pp. 187–224

- G. Faye, T. Giletti and M. Holzer
Asymptotic spreading for Fisher-KPP reaction-diffusion equations with heterogeneous shifting diffusivity (PDF)
Discrete and Continuous Dynamical Systems Series S, 15(2022), no.9 pp. 2467–2496

- C. Besse and G. Faye
Spreading properties for SIR models on homogeneous trees (PDF)
Bulletin of Mathematical Biology, 83:114 (2021) , pp. 1-27

- C. Besse and G. Faye
Dynamics of epidemic spreading on connected graphs (PDF)
Journal of Mathematical Biology 82 (6) (2021) , pp. 1-52

- M. Alfaro, A. Ducrot and G. Faye
Erratum: Quantitative estimates of the threshold phenomena for propagation in reaction-diffusion equations. (PDF)
SIAM J. Appl. Dyn. Syst. 20(1) (2021), pp. 571-572.

- G. Faye, M. Holzer, A. Scheel and L. Siemer
Invasion into remnant instability: a case study of front dynamics (PDF)
Indiana Univ. Math. J., Vol. 71, No. 5, (2022) pp. 1-78.

- G. Faye and M. Holzer
Asymptotic stability of the critical pulled front in a Lotka-Volterra competition model. (PDF)
J. Differential Equations vol 269, issue 9 (2020), pp. 6559-6601.

- M. Alfaro, A. Ducrot and G. Faye
Quantitative estimates of the threshold phenomena for propagation in reaction-diffusion equations. (PDF)
SIAM J. Appl. Dyn. Syst. 19(2) (2020), pp. 1291-1311.

- J. Crevat, G. Faye and F. Filbet
Rigorous derivation of the nonlocal reaction-diffusion FitzHugh-Nagumo system. (PDF)
SIAM J. Math. Anal. 51-1 (2019), pp. 346-373.

- G. Faye and M. Holzer
Asymptotic stability of the critical Fisher-KPP front using pointwise estimates. (PDF)
Zeitschrift für angewandte Mathematik und Physik, 70:13 (2019), pp. 1-25.

- G. Faye and M. Holzer
Bifurcation to locked fronts in two component reaction-diffusion systems. (PDF)
Annales de l'Institut Henri Poincaré (C), Analyse Nonlinéaire, vol 36 (2019), pp. 545-584.

- G. Faye and Z.P. Kilpatrick
Threshold of front propagation in neural fields: An interface dynamics approach. (PDF)
SIAM J. Appl. Math. 78-5 (2018), pp. 2575-2596.

- G. Faye
Traveling fronts for lattice neural field equations. (PDF)
Physica D, 378-379 (2018), pp. 20-32.

- G. Faye and G. Peltier§
Anomalous invasion speed in a system of coupled reaction-diffusion equations. (PDF)
Commun. Math. Sci., Vol. 16, No. 2 (2018), pp. 441-461.

- G. Faye and A. Scheel
Center Manifolds without a Phase Space. (PDF)
Trans. Amer. Math. Soc., 370 (2018), 5843-5885.

- G. Faye, M. Holzer and A. Scheel
Linear spreading speeds from nonlinear resonant interaction. (PDF)
Nonlinearity, vol 30, no 6, (2017), pp. 2403-2442.

- J. Fang and G. Faye
Monotone traveling waves for delayed neural field equations. (PDF)
Mathematical Methods & Models in Applied Sciences, vol 26, no 10 (2016), pp. 1919-1954.

- T. Andreson§, G. Faye, A. Scheel and D. Stauffer§
Pinning and Unpinning in Nonlocal Systems. (PDF)
Journal of Dynamics and Differential Equations, vol 28, issue 3-4, (2016), pp 897-923.

- G. Faye
Multidimensional stability of planar traveling waves for the scalar nonlocal Allen-Cahn equation. (PDF)
Discrete and Continuous Dynamical System A, volume 36, no. 5 (2016), pp. 2473-2496.

- G. Faye and M. Holzer
Modulated traveling fronts for a nonlocal Fisher-KPP equation: a dynamical system approach. (PDF)
J. of Differential Equations, Volume 258, Issue 7, (2015), pp. 2257–2289.

- G. Faye and A. Scheel
Existence of pulses in excitable media with nonlocal coupling. (PDF)
Advances in Mathematics, vol 270 (2015), pp. 400-456.

- C. Browne§ and A.L. Dickerson§ - Mentors: G. Faye and A. Scheel
Coherent Structures in Scalar Feed-Forward Chains. (PDF)
SIAM Undergraduate Research Online, vol 7 (2014), pp. 306-329.

- G. Faye and A. Scheel
Fredholm properties of nonlocal differential equations via spectral flow. (PDF)
Indiana Univ. Math. J., 63 (2014), pp. 1311-1348.

- G. Faye and J. Touboul
Pulsatile localized dynamics in delayed neural-field equations. (PDF)
SIAM J. Appl. Math. 74-5 (2014), pp. 1657-1690.

- Z. Kilpatrick and G. Faye
Pulse bifurcations in stochastic neural fields. (PDF)
SIAM J. Appl. Dyn. Syst., 13(2) (2014), pp. 830-860.

- J. Rankin, D. Avitabile, J. Baladron, G. Faye and D.J. Lloyd
Continuation of localised coherent structures in nonlocal neural field equations. (PDF)
SIAM J. Sci. Comput. 36-1 (2014), pp. B70-B93.

- G. Faye
Existence and stability of traveling pulses of a neural field equation with synaptic depression. (PDF)
SIAM J. Appl. Dyn. Syst., 12-4 (2013), pp. 2032-2067.

- P. Chossat and G. Faye
Pattern formation for the Swift-Hohenberg equation on the hyperbolic plane (PDF)
Journal of Dynamics and Differential Equations, vol 27, Issue 3, (2015), pp. 485-531.

- G. Faye and P. Chossat
A spatialized model of textures perception using structure tensor formalism (PDF)
Networks and Heterogeneous Media, vol 8, issue 1, (2013), pp 211-260

- G. Faye, J. Rankin and D.J. Lloyd
Localized radial bumps of a neural field equation on the Euclidean plane and the Poincaré disk (PDF)
Nonlinearity, 26, (2013), pp 437-478

- G. Faye, J. Rankin and P. Chossat
Localized states in an unbounded neural field equation with smooth firing rate function: a multi-parameter analysis (PDF)
Journal of Mathematical Biology, (2013), vol 66, issue 6, pp 1303-1338

- G. Faye
Reduction method for studying localized solutions of neural field equations on the Poincaré disk (PDF)
C. R. Math. Acad. Sci. Paris, vol 350, issue 3-4, (2012), pp 161-166

- G. Faye and P. Chossat
Bifurcation diagrams and heteroclinic networks of octagonal H-planforms (PDF)
Journal of Nonlinear Science, vol 22, issue 3, (2012), pp 277-325

- G. Faye, P. Chossat and O. Faugeras
Analysis of a hyperbolic geometric model for visual texture perception (PDF)
Journal of Mathematical Neuroscience, 1(4), (2011)

- P. Chossat, G. Faye and O. Faugeras
Bifurcation of Hyperbolic Planforms (PDF)
Journal of Nonlinear Science,vol 21, issue 4, (2011), pp 465-498

- G. Faye and O. Faugeras
Some theoretical and numerical results for delayed neural field equations (PDF)
Physica D,vol 239, issue 9, (2010), pp 561-578

Proceedings


- J.-F. Coulombel and G. Faye
Local limit theorems for complex valued sequences: Old and New (PDF)
Proceedings Journées EDP (2024)

Habilitation manuscript


- G. Faye
Some propagation phenomena in local and nonlocal reaction-diffusion equations - A dynamical systems approach (PDF)

PhD manuscript


- G. Faye
Symmetry breaking and pattern formation in some neural field equations (PDF)