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

2020/05/13 by Yuming Paul Zhang, Zhang, Yuming Paul
Computer Science · Mathematics · #35B65 #35K65 #35R35 #45K05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2005.06668

openalex publication_date 2020/05/13 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We study the free boundary of the porous medium equation with nonlocal drifts\nin dimension one. Under the assumption that the initial data has\nsuper-quadratic growth at the free boundary, we show that the solution is\nsmooth in space and C^2,1 _loc in time, and then the free boundary is\nC^2,1 _loc. Moreover if the drift is local, both the solution and the\nfree boundary are smooth.\n

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