CERMICS – ENPC
6 et 8 avenue Blaise Pascal
Cité Descartes – Champs-sur-Marne
77455 MARNE LA VALLÉE
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.
My CV
I defended my PhD thesis on 11 February 2011 (manuscript). Title: Homogénéisation de modèles cinétiques dans des espaces de phase étendus. (Homogenization of kinetic models in extended phase spaces) PhD supervisors: Claude Bardos and François Golse.
Research interests: Research interests: partial differential equations, kinetic theory, positive semigroups, asymptotic behaviour, and applications to biology.
Teaching: first year mathematics at École nationale supérieure des sciences géographiques and “Mathematical Tools for Engineers” at École des Ponts ParisTech.
Publications:
Bernard Étienne, On the existence and asymptotic behavior of weak solution of the kinetic Fokker-Planck Equation in a bounded domaine with absorbing boundary. Bulletin des Sciences Mathématiques, 197, (2024) (article en open access)
Bernard Étienne and Salvarani Francesco, On the homogenization of the renewal equation with heterogeneous external constraints. Acta Applicandae Mathematicae 187, (2023) (preprint, article)
Bernard Étienne and Salvarani Francesco, Homogenization of the linear Boltzmann Equation with a highly oscillating scattering term in extended phase space, Applied Mathematics Letters, 143 (2023) 108672 (Hal, article)
Bernard Étienne, Loskot-Rudnicki’s inequality and General Relative Entropy inequality for Cauchy problems preserving positivity, Acta Applicandae Mathematicae 180, (2022) (link, ArXiv)
Bernard Étienne, Fathi Max, Levitt Antoine and Stoltz Gabriel, Hypocoercivity with Schur complements, Annales Henri Lebesgue, Volume 5 (2022), pp. 523-557. (preprint, link).
Bernard Étienne and Gabriel Pierre, Asynchronous exponential growth of the growth-fragmentation equation with unbounded fragmentation rate, J. Evol. Equ., 20, 375-401 (2020) (article, preprint)
Bernard Étienne, Doumic Marie, and 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 Étienne, Desvillettes Laurent, Golse François, and 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 Étienne, Desvillettes Laurent, Golse François, and Ricci Valeria, A Derivation of the Vlasov-Navier-Stokes Model for Aerosol Flows from Kinetic Theory, Communications in Mathematical Sciences, 15 (2017), 1703-1741. (article, preprint)
Bernard Étienne and Gabriel Pierre, Asymptotic behavior of the growth-fragmentation equation with bounded fragmentation rate; Journal of Functional Analysis, Vol.272, No.8 (2017), pp. 3455-3485. (article, preprint)
Bardos, Claude; Bernard, Étienne; 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). (article, preprint)
Bernard, Étienne; Salvarani, Francesco, Optimal estimate of the spectral gap for the degenerate Goldstein-Taylor model, J. Stat. Phys., 153, 2 (2013) pp. 363-375 (article, preprint)
Bernard, Étienne; Salvarani, Francesco, On the exponential decay to equilibrium of the degenerate linear Boltzmann equation, J. Funct. Anal. 265, 9 (2013), pp. 1934-1954
Bernard, Étienne; Salvarani, Francesco, On the convergence to equilibrium for degenerate transport problems, Arch. Rational Mech. Anal. 208, 3, (2013) pp. 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, Étienne; 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, Étienne; Golse, François, Salvarani Francesco, Homogenization of transport problems and semigroups, Mathematical Methods in the Applied Sciences, Vol 33, No. 10, pp. 1228-1234 (2010)
Bernard, Étienne; Del Pino Stéphane, Deriaz Erwan, Desprès Bruno, Jurkova Katerina, Lagoutière Frédéric, Lagrangian method enhanced with edge swapping for the free fall and contact problem. ESAIM: Proc., 2008, Vol. 24, pp. 46-59