Localization in stationary non-equilibrium solutions for multicomponent coagulation systems
Abstract
We 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.
Cite
@article{arxiv.2006.14840,
title = {Localization in stationary non-equilibrium solutions for multicomponent coagulation systems},
author = {Marina A. Ferreira and Jani Lukkarinen and Alessia Nota and Juan J. L. Velázquez},
journal= {arXiv preprint arXiv:2006.14840},
year = {2022}
}
Comments
27 pages. The original manuscript has been split. This is a shorter version of the original manuscript containing the Localization Result