Analytical and numerical  results on the positivity of steady state solutions of a thin film  equation

Daniel Ginsberg; Gideon Simpson

doi:10.3934/dcdsb.2013.18.1305

Article Contents

2013, Volume 18, Issue 5: 1305-1321. Doi: 10.3934/dcdsb.2013.18.1305

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Analytical and numerical results on the positivity of steady state solutions of a thin film equation

Daniel Ginsberg^1, and
Gideon Simpson^2,

1.
Department of Mathematics, University of Toronto, Toronto
2.
School of Mathematics, University of Minnesota, Minneapolis, MN, 55455

Received: September 30, 2011

Revised: November 30, 2012

Published: June 2013

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Abstract

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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Mathematics Subject Classification: Primary: 74K35, 65M70; Secondary: 35B09.

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