Finite speed of propagation for the thin film equation in spherical\n geometry

2018/02/06 by Roman M. Taranets, Taranets, Roman
Engineering · Mathematics · Physics and Astronomy · #35B45 #35B65 #35K35 #35K55 #35K65 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Thin Films #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1802.02031

openalex publication_date 2018/02/06 · openalex created_date 2022/08/04 · openalex updated_date 2026/07/28

Abstract

We show that a double degenerate thin film equation, which originated from\nmodeling of viscous coating flow on a spherical surface, has finite speed of\npropagation for nonnegative strong solutions and hence there exists an\ninterface or free boundary separating the regions where solution u>0 and\nu=0. Using local entropy estimates we also obtain an upper bound for the rate\nof the interface propagation.\n

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