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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

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Type
Article accepté pour publication ou publié
Date
2015
Journal name
Kinetic & Related Models
Volume
8
Number
2
Publisher
AIMS - American Institute of Mathematical Sciences
Published in
Paris
Pages
201-214
Publication identifier
Metadata
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Author(s)
Agueh, Martial
Carlier, Guillaume
Illner, Reinhard
Abstract (EN)
We obtain new a priori estimates for spatially inhomogeneous solutions of akinetic equation for granular media, as first proposed in [3]and, more recently,studied in [1]. 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 / Keywords
Kinetic granular media; asymptotic behavior; entropy bounds; global in time estimates