Waiting time of propagation and the backward motion of interfaces in thin-film flow theory

Andrey Shishkov

doi:10.3934/proc.2007.2007.938

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2007, Volume 2007: 938-945. Doi: 10.3934/proc.2007.2007.938 open access

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Waiting time of propagation and the backward motion of interfaces in thin-film flow theory

Andrey Shishkov^1,

1.
Institute of Applied Mathematics and Mechanics, 83114 Donetsk

Received: August 31, 2006

Revised: January 31, 2007

Published: August 2007

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Abstract

Method of difference-functional inequalities in the study of initial propagation of the supports of generalized solutions of higher order quasilinear parabolic equations is described. As application, we find some flatness conditions on the initial function, which guarantee appearance of a waiting time in the propagation and backward motion of interfaces phenomena in thin-film flow type equations. Some lower estimate of backward motion speed is obtained too.

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Mathematics Subject Classification: Primary: 35K35; Secondary: 35K65.

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