Generalized solutions of a kinetic granular media equation by a gradient flow approach

Martial Agueh (1) , Guillaume Carlier (2)

1 PIMS - Pacific Institute for the Mathematical Sciences
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We consider a one-dimensional kinetic model of granular media in the case where the interaction potential is quadratic. Taking advantage of a simple first integral, we can use a reformulation (equivalent to the initial kinetic model for classical solutions) which allows measure solutions. This reformulation has a Wasserstein gradient flow structure (on a possibly infinite product of spaces of measures) for a convex energy which enables us to prove global in time well-posedness.

Mots clés: gradient flows AMS Subject Classifications: 35Q70; 35D30; 35F25; product Wasserstein space; Kinetic models of granular media

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Martial Agueh, Guillaume Carlier. Generalized solutions of a kinetic granular media equation by a gradient flow approach. Calculus of Variations and Partial Differential Equations, 2016. ⟨hal-01164843⟩