On Oscillations of Solutions of the Fourth-Order Thin Film Equation Near Heteroclinic Bifurcation Point

2013/12/10 by Victor A. Galaktionov, Galaktionov, Victor A.
Mathematics · #35K55 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35K55

paper · pdf · doi:10.48550/arxiv.1312.2762

15 pages, 11 Figures

arxiv created 2013/12/10 · arxiv updated 2013/12/11

Abstract

It is shown that solutions of the Cauchy for the fourth-order thin film equation becomes non-oscillatory and non-sign-changing precisely at and above the heteroclinic bifurcation point n=1.75987..., so that, possibly, these solutions begin to coincide with nonnegative solutions of a standard and well-known free-boundary problem.

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