Nonlocal Interaction Equations in Environments with Heterogeneities and Boundaries

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 ob...

Full description

Saved in:
Bibliographic Details
Published inCommunications in partial differential equations Vol. 40; no. 7; pp. 1241 - 1281
Main Authors Wu, Lijiang, Slepčev, Dejan
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis Group 03.07.2015
Taylor & Francis Ltd
Subjects
Boundaries
Equations on manifolds
Gradient flow
Gradient flows
Heterogeneity
Mathematical analysis
Nonlocal interactions
Optimal transport
Partial differential equations
Particle approximation
Stability
Uniqueness
Well-posedness of measure solutions
Online AccessGet full text

Cover

More Information
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0360-5302
1532-4133
DOI:10.1080/03605302.2015.1015033