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1 Dedication Dedicated to the memory of Richard Duun. Abstract The Fokker{Planck equation, or forward Kolmogorov equation, describes the evolution of the probability density for a stochastic process associated with an Ito stochastic diierential equation. It pertains to a wide variety of time{dependent systems in which randomness plays a role. In this paper,… (More)

- J J Jonas, L Kestens, D Wolf, V Yamakov, P Keblinski, S R Phillpotand +77 others
- 2007

- Victor W.Guillemin, David Kinderlehrer, Marc A.Rieffel, Bhama Srinivasan, David W.McLaughlin, Howard Masur +2 others
- 2015

General Description · Committee is standing · Number of members is four or five · Term is four years · Principal Activities This Editorial Committee is charged with selecting for publication by the AMS books which exposit research-level mathematics of current interest to the mathematical community. These books are frequently suitable as texts for an… (More)

Evolution and trend to equilibrium of a (planar) network of grain boundaries subject to curvature driven growth is established under the assumption that the system is initially close to some equilibrium configuration. Curvature driven growth is the primary mechanism in processing polycrystalline materials to achieve desired texture, ductility, toughness,… (More)

- MICHEL CHIPOT, DAVID KINDERLEHRER, MICHAL KOWALCZYK, PIERO VILLAGGIO
- 2002

Intracellular transport in eukarya is attributed to motor proteins that transduce chemical energy into directed mechanical energy. This suggests that, in nonequilibrium systems, fluctuations may be oriented or organized to do work. Here we seek to understand how this is manifested by quantitative mathematical portrayals of these systems.

The flashing rachet is the simplest example of diffusion mediated transport as well as the suggested mechanism for a class of protein motors. Here we briefly explain these concepts and give an entropy based argument for existence and uniqueness of a model problem. We also examine the features of the system that lead to transport

In this note we discuss transport properties of weakly coupled parabolic systems of evolution equations. These arise in the study of molecular motors, like conventional kinesin, which are responsible for eukaryotic intracellular transport. It falls under the rubric of what we call diffusion mediated transport. Diffusion mediated transport generally concerns… (More)

- Adrien Blanchet, José Antonio Carrillo, David Kinderlehrer, Micha l Kowalczyk, Philippe Laurençot, Stefano Lisini
- 2015

We construct weak global in time solutions to the classical Keller-Segel system describing cell movement by chemotaxis in two dimensions when the total mass is below the established critical value. Our construction takes advantage of the fact that the Keller-Segel system can be realized as a gradient flow in a suitable functional product space. This allows… (More)

We prove a contraction in L 1 property for the solutions of a nonlin-ear reaction–diffusion system whose special cases include intercellular transport as well as reversible chemical reactions. Assuming the existence of stationary solutions we show that the solutions stabilize as t tends to infinity. Moreover, in the special case of linear reaction terms, we… (More)