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Convergence to equilibrium in Wasserstein distance for damped Euler equations with interaction forces

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Title: Convergence to equilibrium in Wasserstein distance for damped Euler equations with interaction forces
Authors: Carrillo de la Plata, J
Choi, Y-P
Tse, O
Item Type: Journal Article
Abstract: We develop tools to construct Lyapunov functionals on the space of probability measures in order to investigate the convergence to global equilibrium of a damped Euler system under the influence of external and interaction potential forces with respect to the 2-Wasserstein distance. We also discuss the overdamped limit to a nonlocal equation used in the modelling of granular media with respect to the 2-Wasserstein distance, and provide rigorous proofs for particular examples in one spatial dimension.
Issue Date: 31-Jan-2019
Date of Acceptance: 29-Aug-2018
URI: http://hdl.handle.net/10044/1/62971
DOI: https://doi.org/10.1007/s00220-018-3276-8
ISSN: 0010-3616
Publisher: Springer Verlag
Start Page: 329
End Page: 361
Journal / Book Title: Communications in Mathematical Physics
Volume: 365
Issue: 1
Copyright Statement: © 2018 The Author(s). This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/P031587/1
Keywords: Science & Technology
Physical Sciences
Physics, Mathematical
Physics
NONLINEAR DIFFUSION WAVES
STRONG RELAXATION LIMIT
GLOBAL BV SOLUTIONS
ASYMPTOTIC-BEHAVIOR
CONSERVATION-LAWS
P-SYSTEM
PARTICLE
AGGREGATION
EXISTENCE
ENTROPY
0105 Mathematical Physics
0206 Quantum Physics
0101 Pure Mathematics
Mathematical Physics
Publication Status: Published
Online Publication Date: 2018-10-04
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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