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Cyclic asymptotic behaviour of a population reproducing by fission into two equal parts / Etienne Bernard in Kinetic & Related Models, vol 12 n° 3 (June 2019)  

Public [article]  inKinetic & Related Models > vol 12 n° 3 (June 2019) . - pp 551 - 571 Titre : Cyclic asymptotic behaviour of a population reproducing by fission into two equal parts Type de document : Article/Communication Auteurs : Etienne Bernard , Auteur ; Marie Doumic, Auteur ; Pierre Gabriel, Auteur Année de publication : 2019 Projets : KIBORD / Article en page(s) : pp 551 - 571 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Termes IGN] asymptote [Termes IGN] comportement [Termes IGN] entropie [Termes IGN] oscillation Résumé : (auteur) We study the asymptotic behaviour of the following linear growth-fragmentation equation xxxxxxx and prove that under fairly general assumptions on the division rate B(x),its solution converges towards an oscillatory function, explicitely given by the projection of the initial state on the space generated by the countable set of the dominant eigenvectors of the operator. Despite the lack of hypo-coercivity of the operator, the proof relies on a general relative entropy argument in a convenient weighted L2 space, where well-posedness is obtained via semigroup analysis. We also propose a non-dissipative numerical scheme, able to capture the oscillations. Numéro de notice : A2019-158 Affiliation des auteurs : Géodésie+Ext (mi2018-2019) Thématique : MATHEMATIQUE Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.3934/krm.2019022 En ligne : http://dx.doi.org/10.3934/krm.2019022 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=93294 [article]

Voir aussi

• Cyclic asymptotic behaviour of a population reproducing by fission into two equal parts / Etienne Bernard (2017)    

A derivation of the Vlasov–Navier–Stokes model for aerosol flows from kinetic theory / Etienne Bernard in Communications in Mathematical Sciences, vol 15 n° 6 ([01/09/2017])  

Public [article]  inCommunications in Mathematical Sciences > vol 15 n° 6 [01/09/2017] . - pp 1703 - 1741 Titre : A derivation of the Vlasov–Navier–Stokes model for aerosol flows from kinetic theory Type de document : Article/Communication Auteurs : Etienne Bernard , Auteur ; Laurent Desvillettes, Auteur ; François Golse, Auteur ; Valeria Ricci, Auteur Année de publication : 2017 Projets : KIBORD / Article en page(s) : pp 1703 - 1741 Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Mathématique [Termes IGN] aérosol [Termes IGN] champ de vitesse [Termes IGN] équation de Navier-Stokes [Termes IGN] flux [Termes IGN] gaz [Termes IGN] particule Résumé : (auteur) This article proposes a derivation of the Vlasov–Navier–Stokes system for spray/aerosol flows. The distribution function of the dispersed phase is governed by a Vlasov-equation, while the velocity field of the propellant satisfies the Navier–Stokes equations for incompressible fluids. The dynamics of the dispersed phase and of the propellant are coupled through the drag force exerted by the propellant on the dispersed phase. We present a formal derivation of this model from a multiphase Boltzmann system for a binary gaseous mixture, involving the droplets/dust particles in the dispersed phase as one species, and the gas molecules as the other species. Under suitable assumptions on the collision kernels, we prove that the sequences of solutions to the multiphase Boltzmann system converge to distributional solutions to the Vlasov-Navier–Stokes equation in some appropriate distinguished scaling limit. Specifically, we assume (a) that the mass ratio of the gas molecules to the dust particles/droplets is small, (b) that the thermal speed of the dust particles/droplets is much smaller than that of the gas molecules and (c) that the mass density of the gas and of the dispersed phase are of the same order of magnitude. The class of kernels modelling the interaction between the dispersed phase and the gas includes, among others, elastic collisions and inelastic collisions of the type introduced in [F. Charles: in “Proceedings of the 26th International Symposium on Rarefied Gas Dynamics”, AIP Conf. Proc. 1084:409–414, 2008]. Numéro de notice : A2017-823 Affiliation des auteurs : LASTIG LAREG+Ext (2012-mi2018) Thématique : MATHEMATIQUE Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.4310/CMS.2017.v15.n6.a11 Date de publication en ligne : 28/06/2017 En ligne : http://dx.doi.org/10.4310/CMS.2017.v15.n6.a11 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=89276 [article]

Asymptotic behavior of the growth-fragmentation equation with bounded fragmentation rate / Etienne Bernard in Journal of functional analysis, vol 272 n° 8 (15 April 2017)  

Public [article]  inJournal of functional analysis > vol 272 n° 8 (15 April 2017) . - pp 3455 - 3485 Titre : Asymptotic behavior of the growth-fragmentation equation with bounded fragmentation rate Type de document : Article/Communication Auteurs : Etienne Bernard , Auteur ; Pierre Gabriel, Auteur Année de publication : 2017 Projets : KIBORD / Article en page(s) : pp 3455 - 3485 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Analyse numérique [Termes IGN] analyse fonctionnelle (mathématiques) [Termes IGN] équation intégrale [Termes IGN] invariant Résumé : (Auteur) We are interested in the large time behavior of the solutions to the growth-fragmentation equation. We work in the space of integrable functions weighted with the principal dual eigenfunction of the growth-fragmentation operator. This space is the largest one in which we can expect convergence to the steady size distribution. Although this convergence is known to occur under fairly general conditions on the coefficients of the equation, we prove that it does not happen uniformly with respect to the initial data when the fragmentation rate in bounded. First we get the result for fragmentation kernels which do not form arbitrarily small fragments by taking advantage of the Dyson–Phillips series. Then we extend it to general kernels by using the notion of quasi-compactness and the fact that it is a topological invariant. Numéro de notice : A2017-779 Affiliation des auteurs : LASTIG LAREG+Ext (2012-mi2018) Thématique : MATHEMATIQUE Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1016/j.jfa.2017.01.009 Date de publication en ligne : 31/01/2017 En ligne : https://doi.org/10.1016/j.jfa.2017.01.009 Format de la ressource électronique : URL Article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=88986 [article]

Cyclic asymptotic behaviour of a population reproducing by fission into two equal parts / Etienne Bernard (2017)    

Public contenu dans ArXiv / Université Cornell (Etats-Unis) (1991)   Titre : Cyclic asymptotic behaviour of a population reproducing by fission into two equal parts Type de document : Article/Communication Auteurs : Etienne Bernard , Auteur ; Marie Doumic, Auteur ; Pierre Gabriel, Auteur Mention d'édition : v3 Editeur : Ithaca [New York - Etats-Unis] : ArXiv - Université Cornell Année de publication : 2017 Projets : KIBORD / Format : 21 Langues : Anglais (eng) Résumé : (auteur) We study the asymptotic behaviour of the following linear growth-fragmentation equation xxxxxxx and prove that under fairly general assumptions on the division rate B(x),its solution converges towards an oscillatory function,explicitely given by the projection of the initial state on the space generated by the countable set of the dominant eigenvectors of the operator.Despite the lack of hypo-coercivity of the operator, the proof relies on a general relative entropy argument in a convenient weighted L2 space, where well-posedness is obtained via semigroup analysis. We also propose a non-dissipative numerical scheme, able to capture the oscillations. Numéro de notice : P2017-001 Affiliation des auteurs : LAREG+Ext (1991-2011) Thématique : MATHEMATIQUE Nature : Preprint nature-HAL : Préprint DOI : 10.48550/arXiv.1609.03846 Date de publication en ligne : 02/11/2017 En ligne : https://doi.org/10.48550/arXiv.1609.03846 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=91916

Voir aussi

• Cyclic asymptotic behaviour of a population reproducing by fission into two equal parts / Etienne Bernard in Kinetic & Related Models, vol 12 n° 3 (June 2019)  

Documents numériques

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The diffusion approximation for the linear Boltzmann equation with vanishing scattering coefficient / Claude Bardos in Communications in Mathematical Sciences, vol 13 n° 3 (2014)  

Public [article]  inCommunications in Mathematical Sciences > vol 13 n° 3 (2014) . - pp 641 - 671 Titre : The diffusion approximation for the linear Boltzmann equation with vanishing scattering coefficient Type de document : Article/Communication Auteurs : Claude Bardos, Auteur ; Etienne Bernard , Auteur ; François Golse, Auteur ; Rémi Sentis, Auteur Année de publication : 2014 Article en page(s) : pp 641 - 671 Langues : Anglais (eng) Descripteur : [Termes IGN] approximation [Termes IGN] coefficient de rétrodiffusion [Termes IGN] équation linéaire [Termes IGN] transfert radiatif Résumé : (auteur) The present paper discusses the diffusion approximation of the linear Boltzmann equation in cases where the collision frequency is not uniformly large in the spatial domain. Our results apply for instance to the case of radiative transfer in a composite medium with optically thin inclusions in an optically thick background medium. The equation governing the evolution of the approximate particle density coincides with the limit of the diffusion equation with infinite diffusion coefficient in the optically thin inclusions. Numéro de notice : A2014-781 Affiliation des auteurs : LASTIG LAREG+Ext (2012-mi2018) Thématique : MATHEMATIQUE Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.4310/CMS.2015.v13.n3.a3 Date de publication en ligne : 03/03/2015 En ligne : http://dx.doi.org/10.4310/CMS.2015.v13.n3.a3 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=78593 [article]

On the exponential decay to equilibrium of the degenerate linear Boltzmann equation / Etienne Bernard in Journal of functional analysis, vol 265 n° 9 (November 2013)  

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Optimal estimate of the spectral gap for the degenerate Goldstein-Taylor model / Etienne Bernard in Journal of statistical physics, vol 153 n° 2 (October 2013)  

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On the convergence to equilibrium for degenerate transport problems / Etienne Bernard in Archive for rational mechanics and analysis, vol 208 n° 3 (June 2013)  

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Monitoring seasonal snow dynamics using ground based high resolution photography (Austre Lovénbreen, Svalbard, 79°N) / Etienne Bernard in ISPRS Journal of photogrammetry and remote sensing, vol 75 (January 2013)  

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La théorie cinétique des gaz et la géodésie / Etienne Bernard in Bulletin d'information scientifique et technique de l'IGN, n° 77 (avril 2011) 

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Homogénéisation de modèles cinétiques dans des espaces des phases étendus / Etienne Bernard (2011)  

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Influence of station referencing on the quality of EOP time series / David Coulot (2010)  

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