Supported by NSF through grant DMS 1311414. §undergraduate student.

Publications


- J. Crevat, G. Faye and F. Filbet
Rigorous derivation of the nonlocal reaction-diffusion FitzHugh-Nagumo system. (PDF)
SIAM J. Math. Anal., to appear (2019), pp. 1-29.

- 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, to appear (2018), pp. 1-40.

- 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

PhD manuscript


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