Journal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Volume 100, Issue -, Pages 122-147Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2014.01.010
Keywords
Wasserstein distance; Gradient flows; Aggregation equations; Measure solution
Categories
Funding
- DGI (Spain) [MTM2011-27739-C04-02]
- AGAUR-Generalitat de Catalunya [2009-SGR-345]
- Royal Society through a Wolfson Research Merit Award
- Engineering and Physical Sciences Research Council [EP/K008404/1]
- Azioni Integrate Italia-Spagna [25]
- INDAM-GNAMPA
- Fondation Mathematique Jacques Hadamard
- FP7-IDEAS-ERC-StG [200497 (BioSMA)]
- EPSRC [EP/K008404/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/K008404/1] Funding Source: researchfish
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We deal with a nonlocal interaction equation describing the evolution of a particle density under the effect of a general symmetric pairwise interaction potential, not necessarily in convolution form. We describe the case of a convex (or lambda-convex) potential, possibly not smooth at several points, generalizing the results of Carrillo et al. (2011). We also identify the cases in which the dynamic is still governed by the continuity equation with well-characterized nonlocal velocity field. (C) 2014 Elsevier Ltd. All rights reserved.
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