A global attracting set for nonlocal Kuramoto-Sivashinsky equations arising in interfacial electrohydrodynamics

Document Type

Article

Publication Date

12-1-2006

Abstract

We study a generalized class of nonlocal evolution equations which includes those arising in the modelling of electrified film flow down an inclined plane, with applications in enhanced heat or mass transfer through interfacial turbulence. Global existence and uniqueness results are proved and refined estimates of the radius of the absorbing ball in L2 are obtained in terms of the parameters of the equations (the length of the system and the dimensionless electric field-measuring parameter multiplying the nonlocal term). The established estimates are compared with numerical solutions of the equations which in turn suggest an optimal upper bound for the radius of the absorbing ball. A scaling argument is used to explain this and a general conjecture is made based on extensive computations. © 2007 Cambridge University Press.

Identifier

33744902440 (Scopus)

Publication Title

European Journal of Applied Mathematics

External Full Text Location

https://doi.org/10.1017/S0956792506006760

e-ISSN

14694425

ISSN

09567925

First Page

677

Last Page

703

Issue

6

Volume

17

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