56 citations · 249 across the 40 of their papers we have counts for
5 papers · 2 filters
On volume-preserving crystalline mean curvature flow
Inwon Kim, Dohyun Kwon, Norbert Požár
In this work we consider the global existence of volume-preserving crystalline curvature flow in a non-convex setting. We show that a natural geometric property, associated with re…
A Hele-Shaw limit without monotonicity
Nestor Guillen, Inwon Kim, Antoine Mellet
We study the incompressible limit of the porous medium equation with a right hand side representing either a source or a sink term, and an injection boundary condition. This model…
Darcy's Law with a Source term
Matt Jacobs, Inwon Kim, Jiajun Tong
We introduce a novel variant of the JKO scheme to approximate Darcy's law with a pressure dependent source term. By introducing a new variable that implicitly controls the source t…
The -contraction principle in optimal transport
Matt Jacobs, Inwon Kim, Jiajun Tong
In this work, we use the JKO scheme to approximate a general class of diffusion problems generated by Darcy's law. Although the scheme is now classical, if the energy density is sp…
Interface Dynamics in a Two-phase Tumor Growth Model
Inwon Kim, Jiajun Tong
We study a tumor growth model in two space dimensions, where proliferation of the tumor cells leads to expansion of the tumor domain and migration of surrounding normal tissues int…