Generalized solutions of a kinetic granular media equation by a gradient flow approach
Analysis of PDEs
2015-06-19 v1
Abstract
We consider a one-dimensional kinetic model of granular media in the case where the interaction potential is quadratic. Taking advan- tage of a simple first integral, we can use a reformulation (equivalent to the initial kinetic model for classical solutions) which allows mea- sure 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.
Keywords
Cite
@article{arxiv.1506.05520,
title = {Generalized solutions of a kinetic granular media equation by a gradient flow approach},
author = {Martial Agueh and Guillaume Carlier},
journal= {arXiv preprint arXiv:1506.05520},
year = {2015}
}