Translator Disclaimer
January/February 2018 Transport and equilibrium in non-conservative systems
L. Chayes, H. K. Lei
Adv. Differential Equations 23(1/2): 1-64 (January/February 2018).

Abstract

We study, in finite volume, a grand canonical version of the McKean-Vlasov equation where the total particle content is allowed to vary. The dynamics is anticipated to minimize an appropriate grand canonical free energy; we make this notion precise by introducing a metric on a set of positive Borel measures without pre-prescribed mass and demonstrating that the dynamics is a gradient flow with respect to this metric. Moreover, we develop a JKO-type scheme suitable for these problems. The latter ideas have general applicability to a class of second order non-conservative problems. For this particular system we prove, using the JKO-type scheme, that under certain conditions – not too far from optimal - convergence to the uniform stationary state is exponential with a rate which is independent of the volume. By contrast, in related conservative systems, decay rates scale (at best) with the square of the characteristic length of the system. This suggests that a grand canonical approach may be useful for both theoretical and computational study of large scale systems.

Citation

Download Citation

L. Chayes. H. K. Lei. "Transport and equilibrium in non-conservative systems." Adv. Differential Equations 23 (1/2) 1 - 64, January/February 2018.

Information

Published: January/February 2018
First available in Project Euclid: 26 October 2017

zbMATH: 06822192
MathSciNet: MR3717161

Subjects:
Primary: 35A99, 49Q99, 70F45, 76R99

Rights: Copyright © 2018 Khayyam Publishing, Inc.

JOURNAL ARTICLE
64 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.23 • No. 1/2 • January/February 2018
Back to Top