David Kinderlehrer

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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)
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)
A mesoscale, variational simulation of grain growth in two-dimensions has been used to explore the effects of grain boundary properties on the grain boundary character distribution. Anisotropy in the grain boundary energy has a stronger influence on the grain boundary character distribution than anisotropy in the grain boundary mobility. As grain growth(More)