Remarks on a class of kinetic models of granular media: Asymptotics and entropy bounds
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Abstract
We obtain new a priori estimates for spatially inhomogeneous solutions of a kinetic equation for granular media, as first proposed in [3] and, more recently, studied in [1]. In particular, we show that a family of convex functionals on the phase space is non-increasing along the flow of such equations, and we deduce consequences on the asymptotic behaviour of solutions. Furthermore, using an additional assumption on the interaction kernel and a ``potential for interaction'', we prove a global entropy estimate in the one-dimensional case.
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| Category | Codex | Gemma |
|---|---|---|
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