Nonlocal Interaction Equations in Environments with Heterogeneities and Boundaries

Author: Wu Lijiang   Slepčev Dejan  

Publisher: Taylor & Francis Ltd

E-ISSN: 1532-4133|40|7|1241-1281

ISSN: 0360-5302

Source: Communications in Partial Differential Equations, Vol.40, Iss.7, 2015-07, pp. : 1241-1281

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

We study well-posedness of a class of nonlocal interaction equations with spatially dependent mobility. We also allow for the presence of boundaries and external potentials. Such systems lead to the study of nonlocal interaction equations on subsets ℳ of ℜ d endowed with a Riemannian metric g. We obtain conditions, relating the interaction potential and the geometry, which imply existence, uniqueness and stability of solutions. We study the equations in the setting of gradient flows in the space of probability measures on ℳ endowed with Riemannian 2-Wasserstein metric.