Date | 2014-10-17 |
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Speaker | Hyung Ju Hwang |

Dept. | Department of Mathematics, Postech |

Room | 129-301 |

Time | 16:00-17:00 |

We consider a viscous thin film surrounded by the outer fluid above and
a flat horizontal insulator-coated electrode surface below. Our assumption
is that the film is completely wetting and conducting. We discuss the
global existence of unique solutions perturbed around positive constant
solutions whenever applied voltage is sufficiently small after a finite
time, and the asymptotic behavior of the solutions. Conversely, when applied
voltage is sufficiently large, we show that the solutions around the constant
positive solutions are unstable. Moreover, we find the existence of infinitely
many bifurcation branches of solutions around positive constant solutions at
certain applied voltage and show the stability of nonconstant steady-state
solutions.

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