On self-similar collapse of discontinuous data for thin film equations with doubly degenerate mobility

2009/01/26 by V. A. Galaktionov, Galaktionov, V. A.
Mathematics · #35K40 #35K55 #35K65 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35K40 #msc:35K55 #msc:35K65

paper · pdf · doi:10.48550/arxiv.0901.3989

39 pages, 16 figures

arxiv created 2009/01/26 · arxiv updated 2009/12/01

Abstract

It is shown that a Riemann-type problem with discontinuous data of sign-type for the thin film equation, which degenerates at +1 and -1, admits a self-similar solution. Both FBP and the Cauchy problem (oscillatory solutions near interfaces) settings are taken into account.

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