Etienne Bernard

6 et 8 avenue Blaise Pascal
Cité Descartes – Champs sur Marne

E-mail : etienne[.]bernard[@]enpc[.]fr (remove brackets, of course)
I am a researcher within the team “Modeling, Analysis and Simulation” of CERMICS at École des Ponts ParisTech.


I defended my PhD thesis on 11st February 2011 (manuscript). Title: Homogénéisation de modèles cinétiques dans des espaces de phase étendus. (Homogeneization of kinetic models in extended phase spaces) PhD supervisors: Claude Bardos and François Golse.

Research interests: Partial Differential Equations, kinetic theory, applications to biology.


Teaching: teaching at École nationale supérieure des sciences géographiques.



Bernard Étienne , “On the existence and asymptotic behavior of weak solution of the kinetic Fokker-Planck Equation in a bounded domaine with absorbing boundary.” preprint (submitted)

Bernard Étienne et Salvarani Francesco, “On the homogeneization of the renewal equation with heterogeneous external constraints“. Acta Applicandae Mathematicae 187, (2023)  (preprint, article)

Bernard Étienne et Salvarani Francesco, Homogenization of the linear Boltzmann Equation with a highly oscillating scattering term in extended phase space, accepted in Applied Mathematics Letters, 143 (2023) 108672 (Hal, article)

Bernard Étienne, Loskot-Rudnicki’s inequality and General Relative Entropy inequality for Cauchy problems preserving positivityActa Applicandae Mathematicae 180, (2022)  (linkArXiv)

Bernard Etienne, Fathi Max, Levitt Antoine et Stoltz Gabriel, Hypocoercivity with Schur complements, Annales Henri Lebesgue, Volume 5 (2022), pp. 523-557. (preprint, link).

  Bernard Etienne et Gabriel Pierre. Asynchronous exponential growth of the growth-fragmentation equation with unbounded fragmentation rate, J. Evol. Equ., 20, 375-401 (2020) (article, preprint)

     Bernard Etienne, Doumic Marie, et Gabriel Pierre : Cyclic asymptotic behaviour of a population reproducing by fission into two equal parts, Kinetic and Related Models, 12 (3), 551-571, 2019, (article, preprint)

         Bernard Etienne, Desvillettes Laurent, Golse François, et Ricci Valeria : A Derivation of the Vlasov-Stokes Model for Aerosol Flows from Kinetic Theory, Kinetic and Related Models, 2018, 11 (1) : 43-69. (article, preprint)

              Bernard Etienne, Desvillettes Laurent, Golse François, et Ricci Valeria : A Derivation of the Vlasov-Navier-Stokes Model for Aerosol Flows from Kinetic Theory, Communications in Mathematical Sciences, 15 (2017), 1703-1741. (articlepreprint)

           Bernard Etienne et Gabriel Pierre : Asymptotic behavior of the growth-fragmentation equation with bounded fragmentation rate; Journal of Functional Analysis, Vol.272, No.8 (2017), p.3455-3485. (articlepreprint)

 Bardos, Claude; Bernard, Etienne; Golse, François; Sentis, Rémi :The diffusion approximation for the linear Boltzmann equation with vanishing scattering coefficient; Communications in Mathematical Sciences, Vol. 13, no. 3 (2015). (articlepreprint)

        Bernard, Etienne; Salvarani, Francesco : Optimal estimate of the spectral gap for the degenerate Goldstein-Taylor model, J. Stat. Phys., 153, 2 (2013) 363-375 (article, preprint)

     Bernard, Etienne; Salvarani, Francesco, On the exponential decay to equilibrium of the degenerate linear Boltzmann equation, J. Funct. Anal. 265, 9 (2013), 1934-1954

    Bernard, Etienne; Salvarani, Francesco : On the convergence to equilibrium for degenerate transport problems, Arch. Rational Mech. Anal. 208, 3, (2013) 977-984

        Coulot D., E. Bernard, X. Collilieux, Influence of station referencing on the quality of EOP time series, Journées 2010 “Systèmes de Référence Spatio-temporels”, page 163, Observatoire de Paris, (2011)

        Bernard, Etienne; Caglioti Emmanuele, Golse, François : Homogenization of the linear Boltzmann equation in a domain with a periodic distribution of holes SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2010, 42, (5), pp. 2082-2113.

        Bernard, Etienne; Golse, François, Salvarani Francesco : Homogenization of transport problems and semigroups, Mathematical Methods in the Applied Sciences, Vol 33, number 10, pp. 1228-1234 (2010)

        Bernard, Etienne; Del Pino Stéphane, Deriaz Erwan, Desprès Bruno, Jurkova Katerina, Lagoutière Frédéric : Lagrangian method enhanced with edge swapping for the free fail and contact problem. ESAIM: Proc., 2008, Vol. 24, pp. 46-59