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Contractions in the 2-Wasserstein length space and thermalization of granular media. (English) Zbl 1082.76105
Summary: An algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a spatially homogeneous flow-through model representing the continuum limit of a gas of particles interacting through slightly inelastic collisions. This rate is obtained by reformulating the dynamical problem as the gradient flow of a convex energy on an infinite-dimensional manifold. An abstract theory is developed for gradient flows in length spaces, which shows how degenerate convexity (or even non-convexity) – if uniformly controlled – quantify contractivity (limit expansivity) of the flow.

76T25 Granular flows
74E20 Granularity
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