Electrified thin films: Global existence of non-negative solutions

Electrified thin films: Global existence of non-negative solutions

We consider an equation modeling the evolution of a viscous liquid thin film wetting a horizontal solid substrate destabilized by an electric field normal to the substrate. The effects of the electric field are modeled by a lower order non-local term. We introduce the good functional analysis framework to study this equation on a bounded domain and prove the existence of weak solutions defined ...

Nonlinear Dynamics of Electrified Thin Liquid Films

We study a nonlinear nonlocal evolution equation describing the hydrodynamics of thin films in the presence of normal electric fields. The liquid film is assumed to be perfectly conducting and to completely wet the upper or lower surface of a horizontal flat plate. The flat plate is held at constant voltage, and a vertical electric field is generated by a second parallel electrode kept at a dif...

architecture and engineering of nanoscale sculptured thin films and determination of their properties

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Global Non { Negative Solutions of a NonlinearFourth { Order

Global Non { Negative Solutions of a NonlinearFourth { Order