# American Institute of Mathematical Sciences

2007, 2007(Special): 938-945. doi: 10.3934/proc.2007.2007.938

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

 1 Institute of Applied Mathematics and Mechanics, 83114 Donetsk, Ukraine

Received  September 2006 Revised  February 2007 Published  September 2007

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.
Citation: Andrey Shishkov. Waiting time of propagation and the backward motion of interfaces in thin-film flow theory. Conference Publications, 2007, 2007 (Special) : 938-945. doi: 10.3934/proc.2007.2007.938
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