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

Pages: 938 - 945, Issue Special, September 2007

 Abstract        Full Text (210.2K)              

Andrey Shishkov - Institute of Applied Mathematics and Mechanics, 83114 Donetsk, Ukraine (email)

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.

Keywords:  Thin-film equation, initial-boundary Neumann problem, propagation of support,backward motion,local entropy estimates, nonnegative strong solution.
Mathematics Subject Classification:  Primary: 35K35; Secondary: 35K65.

Received: September 2006;      Revised: February 2007;      Published: September 2007.