# Science at the triple point between mathematics, mechanics and materials science

## Publication 121

### Nonlocal Interaction Equations in Environments with Heterogeneities and Boundaries

##### Authors:

Lijiang Wu
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213

Dejan Slepčev
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213

##### 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.
##### Get the paper in its entirety
13-CNA-023.pdf

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