Convergence to equilibrium for a thin-film equation

Series: 
Math Physics Seminar
Wednesday, February 23, 2011 - 16:30
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
Department of Mathematics, University of Toronto
Organizer: 
I will describe recent work with Marina Chugunovaand Ben Stephens on the evolution of a thin-filmequation that models a "coating flow" on a horizontalcylinder. Formally, the equation defines a gradientflow with respect to an energy that controls theH^1-norm.We show that for each given mass there exists aunique steady state, given by a droplet hanging from thebottom of the cylinder that meets the dry region withzero contact angle.  The droplet minimizes the energy andattracts all strong solutions that satisfy certain energyand entropy inequalities.  (Such solutions exist for arbitraryinitial values of finite energy and entropy, but it is notknown if they are unique.) The distance of any solutionfrom the steady state decays no faster than a power law.