Date of Original Version
This is an Accepted Manuscript of an article published by Taylor & Francis Group available online at: http://www.tandfonline.com/10.1080/03605302.2015.1015033.
Abstract or Description
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.
Communications in Partial Differential Equations, 40, 7, 1241-1281.