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arXiv · 1708.05842

Singular limit of the porous medium equation with a drift

Inwon Kim·Norbert Požár·Brent Woodhouse
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Abstract

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 presence of a drift and the consequent lack of monotonicity in time. In the limit a Hele-Shaw-type free boundary problem emerges, which describes the evolution of the congested zone where density equals one. We discuss pointwise convergence of the densities as well as the $BV$ regularity of the limiting free boundary.

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Inwon Kim, Norbert Požár, Brent Woodhouse. 2017-08-19. Singular limit of the porous medium equation with a drift. https://arxiv.org/abs/1708.05842

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