Analytical and Numerical Results on the Positivity of Steady State Solutions of a Thin Film Equation

Details Analytical and Numerical Results on the Positivity of Steady State Solutions of a Thin Film Equation Analytical and Numerical Results on the Positivity of Steady State Solutions of a Thin Film Equation

2011-01-17

arxiv.org/abs/1101.3261v2

Mathematics

Analysis of PDEs

17 pages, 12 figures

Scientific paper

We consider an equation for a thin-film of fluid on a rotating cylinder and present several new analytical and numerical results on steady state solutions. First, we provide an elementary proof that both weak and classical steady states must be strictly positive so long as the speed of rotation is nonzero. Next, we formulate an iterative spectral algorithm for computing these steady states. Finally, we explore a non-existence inequality for steady state solutions from the recent work of Chugunova, Pugh, & Taranets.

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