Nonlocal Interaction Equations in Environments with Heterogeneities and Boundaries |
| |
Authors: | Lijiang Wu Dejan Slep?ev |
| |
Institution: | Department of Mathematical Sciences , Carnegie Mellon University , Pittsburgh , Pennsylvania , USA |
| |
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 ? of ? 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 ? endowed with Riemannian 2-Wasserstein metric. |
| |
Keywords: | Equations on manifolds Gradient flows Nonlocal interactions Optimal transport Particle approximation Well-posedness of measure solutions |
|
|