| Abstract: |
| In this talk, I will present results concerning the singular limit of
the solutions of the porous medium equations with a drift. Under the
assumption that the drift field is compressive, we show that, in the
incompressible limit, the solutions converge to the solution of a
constrained transport equation with no diffusion. The limit solution
reaches the constraint in a so-called congested set, which can be
characterized by a certain Hele-Shaw type problem. This convergence
result establishes the relationship of the diffuse interface models and
sharp interface models of crowd motion and tumor growth. This is joint
work with Inwon Kim and Brent Woodhouse. |
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