Interpreting systems of continuity equations in spaces of probability measures through PDE duality
Analysis of PDEs
2024-06-05 v3
Abstract
We introduce a notion of duality solution for a single or a system of transport equations in spaces of probability measures reminiscent of the viscosity solution notion for nonlinear parabolic equations. Our notion of solution by duality is, under suitable assumptions, equivalent to gradient flow solutions in case the single/system of equations has this structure. In contrast, we can deal with a quite general system of nonlinear nonlocal, diffusive or not, system of PDEs without any variational structure.
Keywords
Cite
@article{arxiv.2206.03968,
title = {Interpreting systems of continuity equations in spaces of probability measures through PDE duality},
author = {José A. Carrillo and David Gómez-Castro},
journal= {arXiv preprint arXiv:2206.03968},
year = {2024}
}