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arXiv · 2005.06668

Free Boundary Regularity of the Porous Medium Equation with nonlocal drifts in Dimension One

Yuming Paul Zhang
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Abstract

We study the free boundary of the porous medium equation with nonlocal drifts in dimension one. Under the assumption that the initial data has super-quadratic growth at the free boundary, we show that the solution is smooth in space and $C^{2,1}_{\loc}$ in time, and then the free boundary is $C^{2,1}_{\loc}$. Moreover if the drift is local, both the solution and the free boundary are smooth.

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Yuming Paul Zhang. 2020-05-13. Free Boundary Regularity of the Porous Medium Equation with nonlocal drifts in Dimension One. https://arxiv.org/abs/2005.06668

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