Grégoire Nadin

Research interests

• Reaction-diffusion equations and propagation phenomenon in space-time 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: Flux-limited solutions (arXiv.org)

• On the instability of threshold solutions of reaction-diffusion 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 non-linear equations via a Laplace type method and two-scales 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) Large-scale asymptotics of velocity-jump processes and nonlocal Hamilton–Jacobi equations, J. London Math. Soc., 108: 141-189, 2023, (arXiv.org),
• Optimization of the L1 norm of the solution of a Fisher-KPP equations in the small diffusivity regime, to appear in Proc. Am. Math. Soc.(arXiv.org)
• (Jeulin et al) Anti-spike IgG antibody kinetics following the second and third doses of BNT162b2 vaccine in nursing home residents, Journal of American geriatrics society, 70(9):2552-2560, 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: bang-bang property and fragmentation rate. Com. PDE, pages 797-828, 47, 2022 (hal).
• (with I. Mazari, and Y. Privat) Shape optimization of a weighted two-phase Dirichlet eigenvalue, Archive for Rational Mechanics and Analysis, Vol. 243, pages 95-137, 2022 (hal)
• (with F. Hamel) Diameters of the level sets for reaction-diffusion equations in nonperiodic slowly varying media, Proc. Amer. Math. Soc., 150 (2022), 3549-3564 . (hal)
• (with E. Ogier-Denis, 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: Two-scale expansions and symmetrisations, Nonlinearity, 34-11 (2021), 7510-7539. (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 reaction-diffusion equations with respect to their initial data, Math. Model. Nat. Phenom. Volume 15, 2020. ⟨hal-02175063⟩
• (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 1-35 (hal).
• (with C. Carrere) Influence of mutations in phenotypically-structured populations in time periodic environment, Discrete & Continuous Dynamical Systems - B, 2020, 25(9): 3609-3630. ⟨hal-02273079⟩
• (with M. Strugarek and N. Vauchelet) Hindrances to bistable front propagation: application to Wolbachia invasion, J. Math. Biol. 76(6), pp 1489-1533, 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 98-156, arXiv.org.
• (with L. Rossi) Transition waves for Fisher-KPP equations with general time-heterogeneous and space-periodic coefficients, Analysis & PDE 8(6) (2015), pp 1351--1377, preprint.
• (with L. Rossi) Generalized transition fronts for one-dimensional almost periodic Fisher-KPP equations, Arch. Rat. Mec. Anal. 223(3) (2017), pp 1239-1267, 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 845--872, preprint.
• How does the spreading speed associated with the Fisher-KPP equation depend on random stationary diffusion and reaction terms?  Discrete Contin. Dyn. Syst. Ser. B, 20 (2015), no. 6, 1785-1803. (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, 1843-1872 arXiv.org
• (with E. Bouin and V. Calvez) Front propagation in a kinetic reaction-transport equation, Archives of rational mechanics and analysis, Springer-Verlag, 217(2), 2015, pp.571-617 (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, 1194--1218 (hal).
• Critical travelling waves for general heterogeneous one-dimensional reaction-diffusion equations, to appear in Annales IHP (PDF)
• (with A. Ducrot) Asymptotic behaviour of travelling waves for the delayed Fisher-KPP equation, Journal of differential equations 256(9) (2014) pp 3115-3140(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) Wave-like solutions for nonlocal reaction-diffusion equations: a toy model, Mathematical Modelling of Natural Phenomena, 08 (2013), pp 33-41 (PDF)
• (with H. Berestycki) Spreading speeds for one-dimensional monostable reaction-diffusion equations, J. Math. Phys. 53(11) (2012) (PDF)
• (with J. Garnier and T. Giletti) Maximal and minimal spreading speeds  for reaction-diffusion equations in nonperiodic slowly varying media, J. Dynam. Differential Equations 24(3) (2012), pp 521-538. arXiv.org. 
• (with L. Rossi) Propagation phenomena for time heterogeneous KPP reaction-diffusion equations, J. Math. Pures Appl. 98(6) (2012), pp 633-653 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 1229-124 (PDF).
• (with F. Hamel) Spreading properties for the Fisher-KPP equation with oscillating initial data, Comm. Part. Diff. Equations 37 (2012), pp 511-537 (preprint on Hal).
• Some dependence results between the spreading speed and the coefficients of the space-time periodic Fisher-KPP equation, Eur. J. Appl. Math. 22 (2011) pp 169-185, (arXiv.org)
• Existence and uniqueness of the solutions of a space-time periodic reaction-diffusion equation, J. Diff. Eq. 249(6) (2010), pp 1288-1304 (preprint).
• The effect of the Schwarz rearrangement on the periodic principal eigenvalue of a nonsymmetric operator, SIAM J. Math. Anal. 4 (2010), pp. 2388-2406 (arXiv.org)
• (with H. Berestycki, B. Perthame, L. Ryzhik) The non-local Fisher-KPP equation: traveling waves and steady states (2009), Nonlinearity 22 (2009), pp 2813-2844 (PDF)
• Traveling fronts in space-time periodic media, J. Math. Pures Appl. 92 (2009), pp 232-262 (arXiv.org)
• The principal eigenvalue of a space-time periodic parabolic operator, Ann. Mat. Pura Appl. 188(4) (2009), pp 269-295 (PDF).
• (with H. Berestycki, F. Hamel) Asymptotic spreading in heterogeneous diffusive excitable media, Journal of Functional Analysis 255 (2008), pp 2146-2189 (link)
• (with B. Perthame, L. Ryzhik) Traveling waves for the Keller-Segel system with Fisher birth terms, Interface free bound. 10 (2008), pp 517-538 (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 553-557 arXiv.org
• Pulsating traveling fronts in space-time periodic media, C.R. Acad. Sci. Paris I 346 (2008), pp 951-956  (PDF)
• Reaction-diffusion equations in space-time periodic media, C.R. Acad. Sci. Paris I 345 (2007), pp 489-493 (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.