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Space-time geometry of Hele-Shaw flow
Carson Collins, Inwon Kim, Sebastian Munoz
We study the dynamic behavior of the free boundary of the Hele-Shaw flow with a nonnegative source, in which the pressure satisfies in and the free boundary moves…
Rate independent capillary motion on a narrow Wilhelmy plate
Carson Collins, William M Feldman
We study a rate independent energetic model of the Wilhelmy plate experiment in capillarity. The evolution is driven by vertical motions of the plate. We show stability of energy s…
Minimizing movements solutions for a monotone model of droplet motion
Carson Collins, William M Feldman
We study the uniqueness and regularity of minimizing movements solutions of a droplet model in the case of piecewise monotone forcing. We show that such solutions evolve uniquely o…
Free boundary regularity for tumor growth with nutrients and diffusion
Carson Collins, Matt Jacobs, Inwon Kim
In this paper, we study a tumor growth model where the growth is driven by nutrient availability and the tumor expands according to Darcy's law with a mechanical pressure resulting…