Abstract
AbstractWe consider the multicomponent Smoluchowski coagulation equation under non-equilibrium conditions induced either by a source term or via a constant flux constraint. We prove that the corresponding stationary non-equilibrium solutions have a universal localization property. More precisely, we show that these solutions asymptotically localize into a direction determined by the source or by a flux constraint: the ratio between monomers of a given type to the total number of monomers in the cluster becomes ever closer to a predetermined ratio as the cluster size is increased. The assumptions on the coagulation kernel are quite general, with isotropic power law bounds. The proof relies on a particular measure concentration estimate and on the control of asymptotic scaling of the solutions which is allowed by previously derived estimates on the mass current observable of the system.
Funder
Università degli Studi dell’Aquila
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Reference11 articles.
1. Banasiak, J., Lamb, W., Laurencot, P.: Analytic Methods for Coagulation-Fragmentation Models. CRC Press, Boca Raton (2019)
2. Degond, P., Liu, J., Pego, R.L.: Coagulation-fragmentation model for animal group-size statistics. J. Nonlinear Sci. 27, 379–424 (2017)
3. Friedlander, S.K.: Smoke, Dust, and Haze. Oxford University Press, Oxford (2000)
4. Ferreira, M.A., Lukkarinen, J., Nota, A., Velázquez, J.J.L.: Stationary non-equilibrium solutions for coagulation systems. Arch. Ration. Mech. Anal. (2021). https://doi.org/10.1007/s00205-021-01623-w
5. Ferreira, M.A., Lukkarinen, J., Nota, A., Velázquez, J.J.L.: Multicomponent coagulation systems: existence and non-existence of stationary non-equilibrium solutions (2021). arXiv:2103.12763
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献