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KIBORD Modèles cinétiques en biologie et domaines connexes
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Affiner la recherche Interroger des sources externesCyclic asymptotic behaviour of a population reproducing by fission into two equal parts / Etienne Bernard in Kinetic & Related Models, vol 12 n° 3 (June 2019)
Titre : Cyclic asymptotic behaviour of a population reproducing by fission into two equal parts Type de document : Article/Communication Auteurs : Etienne Bernard 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] oscillationRésumé : (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
in Kinetic & Related Models > vol 12 n° 3 (June 2019) . - pp 551 - 571[article]
Titre : A derivation of the Vlasov–Navier–Stokes model for aerosol flows from kinetic theory Type de document : Article/Communication Auteurs : Etienne Bernard 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] particuleRésumé : (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
in Communications in Mathematical Sciences > vol 15 n° 6 [01/09/2017] . - pp 1703 - 1741[article]
Titre : Asymptotic behavior of the growth-fragmentation equation with bounded fragmentation rate Type de document : Article/Communication Auteurs : Etienne Bernard 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] invariantRésumé : (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
in Journal of functional analysis > vol 272 n° 8 (15 April 2017) . - pp 3455 - 3485[article]
Titre : Cyclic asymptotic behaviour of a population reproducing by fission into two equal parts Type de document : Article/Communication Auteurs : Etienne Bernard 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 Documents numériques
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