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We consider a one-dimensional kinetic model of granular media in the casewhere the interaction potential is quadratic. Taking advan- tage of a simplefirst integral, we can use a reformulation (equivalent to the initial kineticmodel for classical solutions) which allows mea- sure solutions. Thisreformulation has a Wasserstein gradient flow structure (on a possibly infiniteproduct of spaces of measures) for a convex energy which enables us to proveglobal in time well-posedness.

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