56 citations · 249 across the 40 of their papers we have counts for
4 papers · 2 filters
Regularity Properties of Degenerate Diffusion Equations with Drifts
Inwon Kim, Yuming Zhang
This paper considers a class of nonlinear, degenerate drift- diffusion equations. We study well-posedness and regularity properties of the solutions, with the goal to achieve unifo…
Singular limit of the porous medium equation with a drift
Inwon Kim, Norbert Požár, Brent Woodhouse
We study the "stiff pressure limit" of a nonlinear drift-diffusion equation, where the density is constrained to stay below the maximal value one. The challenge lies in the presenc…
On nonlinear cross-diffusion systems: an optimal transport approach
Inwon Kim, Alpár R. Mészáros
We study a nonlinear, degenerate cross-diffusion model which involves two densities with two different drift velocities. A general framework is introduced based on its gradient flo…
Uniform convergence for the incompressible limit of a tumor growth model
Inwon Kim, Olga Turanova
We study a model introduced by Perthame and Vauchelet that describes the growth of a tumor governed by Brinkman's Law, which takes into account friction between the tumor cells. We…