Research interests
 Reactiondiffusion equations and propagation phenomenon in spacetime heterogeneous media
 Principal eigenvalues of elliptic and parabolic operators
 Optimization and control of PDE in life sciences
 Mathematical models in biology and ecology
Preprints

(with K.Y. Lam and X. Yu) Asymptotic spreading of KPP reactive fronts in heterogeneous shifting environments II: Fluxlimited solutions (arXiv.org)

On the instability of threshold solutions of reactiondiffusion equations, and applications to optimization problems (Hal)

Gaussian estimates for general parabolic operators in dimension 1 (arXiv.org)
 (with I. Mazari) Optimality conditions for the linear optimal control of nonlinear equations via a Laplace type method and twoscales like expansions (arXiv.org)
Publications (also on Hal)
 (with Luis Almeida, Alexis Leculier, and Yannick Privat) Optimal control of bistable travelling waves: looking for the best spatial distribution of a killing action to block a pest invasion, SIAM J. Control Optim. 62, No. 2, 1291–1315 (2024) (Hal).
 (with E. Bouin, V. Calvez, and E. Grenie) Largescale asymptotics of velocityjump processes and nonlocal Hamilton–Jacobi equations, J. London Math. Soc., 108: 141189, 2023, (arXiv.org),
 Optimization of the L1 norm of the solution of a FisherKPP equations in the small diffusivity regime, to appear in Proc. Am. Math. Soc.(arXiv.org)
 (Jeulin et al) Antispike IgG antibody kinetics following the second and third doses of BNT162b2 vaccine in nursing home residents, Journal of American geriatrics society, 70(9):25522560, 2022 (medrXiv).
 (with H. Berestycki) Asymptotic spreading for general heterogeneous equations, Memoirs of the American Mathematical Society, American Mathematical Society, 280(1381), 2022 (hal).
 (with I. Mazari, and Y. Privat) Optimisation of the total population size for logistic diffusive equations: bangbang property and fragmentation rate. Com. PDE, pages 797828, 47, 2022 (hal).
 (with I. Mazari, and Y. Privat) Shape optimization of a weighted twophase Dirichlet eigenvalue, Archive for Rational Mechanics and Analysis, Vol. 243, pages 95137, 2022 (hal)
 (with F. Hamel) Diameters of the level sets for reactiondiffusion equations in nonperiodic slowly varying media, Proc. Amer. Math. Soc., 150 (2022), 35493564 . (hal)
 (with E. OgierDenis, A. I. Toledo Marrero, H. Zaag) A Turing mechanism in order to explain the patchy nature of Crohn's disease, Journal of Mathematical Biology, Vol 83(2), 2021 (hal)
 (with I. Mazari, and A. I. Toledo Marrero) Optimisation of the total population size with respect to the initial condition for semilinear parabolic equations: Twoscale expansions and symmetrisations, Nonlinearity, 3411 (2021), 75107539. (hal)
 (with L. Almeida, P.A. Bliman, B. Perthame, and N. Vauchelet) Final size and convergence rate for an epidemic in heterogeneous population, Math. Models and Meth. in Appl. Sci., 2021. (hal)
 (with A. I. Toledo Marrero) On the maximization problem for solutions of reactiondiffusion equations with respect to their initial data, Math. Model. Nat. Phenom. Volume 15, 2020. ⟨hal02175063⟩
 (with I. Mazari, and Y. Privat) Optimal location of resources maximizing the total population size in logistic models, Journal de Mathematiques Pures et Appliquees, Elsevier, February 2020, Pages 135 (hal).
 (with C. Carrere) Influence of mutations in phenotypicallystructured populations in time periodic environment, Discrete & Continuous Dynamical Systems  B, 2020, 25(9): 36093630. ⟨hal02273079⟩
 (with M. Strugarek and N. Vauchelet) Hindrances to bistable front propagation: application to Wolbachia invasion, J. Math. Biol. 76(6), pp 14891533, arXiv.org.
 (with L. Girardin) Competition in periodic media: II  Segregative limit of pulsating fronts and "Unity is not Strength"type result, Journal of Differential equations 265(01) (2018) pp 98156, arXiv.org.
 (with L. Rossi) Transition waves for FisherKPP equations with general timeheterogeneous and spaceperiodic coefficients, Analysis & PDE 8(6) (2015), pp 13511377, preprint.
 (with L. Rossi) Generalized transition fronts for onedimensional almost periodic FisherKPP equations, Arch. Rat. Mec. Anal. 223(3) (2017), pp 12391267, arXiv.org.
 (with J. Lamboley, A. Laurain, and Y. Privat) Properties of optimizers of the principal eigenvalue with indefinite weight and Robin conditions, Calc. Var. Partial Differential Equations 55 (2016), no. 6. arXiv.org.
 (with Y. Privat) An extremal eigenvalue problem arising in heat conduction, J. Math. Pures Appl. (9) 105 (2016), no. 6, pp 845872, preprint.
 How does the spreading speed associated with the FisherKPP equation depend on random stationary diffusion and reaction terms? Discrete Contin. Dyn. Syst. Ser. B, 20 (2015), no. 6, 17851803. (PDF)
 (with L. Girardin) Travelling waves for diffusive and strongly competitve systems: relative motility and invasion speed. Accepted for publication in Eur. J. Appl. Math. (arXiv).
 (with J. Bouhours) A variational approach to reaction diffusion equations with forced speed in dimension 1. Discrete Contin. Dyn. Syst. A 35 (2015), no. 5, 18431872 arXiv.org
 (with E. Bouin and V. Calvez) Front propagation in a kinetic reactiontransport equation, Archives of rational mechanics and analysis, SpringerVerlag, 217(2), 2015, pp.571617 (hal).
 (with G. Mark and Y. Privat) What is the optimal shape of a fin for stationary heat conduction? SIAM J. Applied Math 74 (2014), no. 4, 11941218 (hal).
 Critical travelling waves for general heterogeneous onedimensional reactiondiffusion equations, to appear in Annales IHP (PDF)
 (with A. Ducrot) Asymptotic behaviour of travelling waves for the delayed FisherKPP equation, Journal of differential equations 256(9) (2014) pp 31153140(PDF).
 (with M. Cristofol, I. Kaddouri and L. Roques). Coefficient determination via asymptotic spreading speeds, Inverse problems 30 (2014) (Hal)
 (with E. Bouin and V. Calvez) Hyperbolic traveling waves driven by growth, accepted for publication in M3AS, arXiv.org
 (with C. Hauzy, E. Canard, I. Gounand, N. Mouquet, B. Ebenman) Confronting the paradox of enrichment to the metacommunity perspective, PLOS One, 8(12) (2013) (link)
 (with L. Rossi, L. Ryzhik and B. Perthame) Wavelike solutions for nonlocal reactiondiffusion equations: a toy model, Mathematical Modelling of Natural Phenomena, 08 (2013), pp 3341 (PDF)
 (with H. Berestycki) Spreading speeds for onedimensional monostable reactiondiffusion equations, J. Math. Phys. 53(11) (2012) (PDF)
 (with J. Garnier and T. Giletti) Maximal and minimal spreading speeds for reactiondiffusion equations in nonperiodic slowly varying media, J. Dynam. Differential Equations 24(3) (2012), pp 521538. arXiv.org.
 (with L. Rossi) Propagation phenomena for time heterogeneous KPP reactiondiffusion equations, J. Math. Pures Appl. 98(6) (2012), pp 633653 arXiv.org.
 (with F. Hamel, L. Roques) A viscosity solution method for the spreading speed formula in slowly varying media, Indiana Univ. Math. J. 60 (2011), pp 1229124 (PDF).
 (with F. Hamel) Spreading properties for the FisherKPP equation with oscillating initial data, Comm. Part. Diff. Equations 37 (2012), pp 511537 (preprint on Hal).
 Some dependence results between the spreading speed and the coefficients of the spacetime periodic FisherKPP equation, Eur. J. Appl. Math. 22 (2011) pp 169185, (arXiv.org)
 Existence and uniqueness of the solutions of a spacetime periodic reactiondiffusion equation, J. Diff. Eq. 249(6) (2010), pp 12881304 (preprint).
 The effect of the Schwarz rearrangement on the periodic principal eigenvalue of a nonsymmetric operator, SIAM J. Math. Anal. 4 (2010), pp. 23882406 (arXiv.org)
 (with H. Berestycki, B. Perthame, L. Ryzhik) The nonlocal FisherKPP equation: traveling waves and steady states (2009), Nonlinearity 22 (2009), pp 28132844 (PDF)
 Traveling fronts in spacetime periodic media, J. Math. Pures Appl. 92 (2009), pp 232262 (arXiv.org)
 The principal eigenvalue of a spacetime periodic parabolic operator, Ann. Mat. Pura Appl. 188(4) (2009), pp 269295 (PDF).
 (with H. Berestycki, F. Hamel) Asymptotic spreading in heterogeneous diffusive excitable media, Journal of Functional Analysis 255 (2008), pp 21462189 (link)
 (with B. Perthame, L. Ryzhik) Traveling waves for the KellerSegel system with Fisher birth terms, Interface free bound. 10 (2008), pp 517538 (PDF)
Notes and proceedings
 (with I. Mazari, and Y. Privat) Optimal control of resources for species survival, 89th GAMM Annual Meeting, Mar 2018, munich, Germany (hal)
 (with B. Perthame and M. Tang) Can a traveling wave connect two unstable states? The case of the nonlocal Fisher equation, C.R. Acad. Sci. Paris I 349 (2010), pp 553557 arXiv.org
 Pulsating traveling fronts in spacetime periodic media, C.R. Acad. Sci. Paris I 346 (2008), pp 951956 (PDF)
 Reactiondiffusion equations in spacetime periodic media, C.R. Acad. Sci. Paris I 345 (2007), pp 489493 (PDF)
Book chapters
 (with I. Mazari, and Y. Privat) Some challenging optimisation problems for logistic diffusive equations and numerical issues, Handbook of Numerical Analysis, Volume 23, 2022 (hal)
 Modelling of Neolithic populations, in Interactions in complex dynamical systems, 2017.
Habilitation à diriger des recherches
I have defended my HDR on June 28th 2018.
Manuscript : french, english.
PhD Thesis
I have defended my PhD (advisors: H. Berestycki and F. Hamel) on november 28, 2008, at ENS Paris.