Remarks on a class of kinetic models of granular media: asymptotics and entropy bounds
Agueh, Martial; Carlier, Guillaume; Illner, Reinhard (2015), Remarks on a class of kinetic models of granular media: asymptotics and entropy bounds, Kinetic & Related Models, 8, 2, p. 201-214. 10.3934/krm.2015.8.201
TypeArticle accepté pour publication ou publié
Journal nameKinetic & Related Models
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Abstract (EN)We obtain new a priori estimates for spatially inhomogeneous solutions of akinetic equation for granular media, as first proposed in and, more recently,studied in . In particular, we show that a family of convexfunctionals on thephase space is non-increasing along the flow of such equations, and we deduceconsequences on the asymptotic behaviour of solutions. Furthermore, using anadditional assumption on the interaction kernel and a “potential for interaction”,we prove a global entropy estimate in the one-dimensional case.
Subjects / KeywordsKinetic granular media; asymptotic behavior; entropy bounds; global in time estimates
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