PDE Seminars 2005-2006

Embedding properties for Weighted-Sobolev spaces in unbounded domains Friday, 8/12/2005, 3:00 PM-4:00 PM
Colloquium/PDE Seminar Speaker: Hirokazu Ohya Department of Mathematics, Waseda University, Japan I am concerned with the embedding properties of certain functional spaces in unbounded domains. In this talk we discuss about Weighted-Sobolev (Banach) spaces with unbounded coefficients, especially for exponentially growing ones. In such cases, Escobedo and Kavian have shown the properties of continuous and compact embedding of Weighted-Sobolev (Hilbert) spaces with simple calculations. By using similar arguments given in above, we can derive (or relax) the sufficient conditions on these coefficients where the embedding properties work well. The above properties are used in showing the existence of solutions for some quasilinear elliptic problems in unbounded domains. I also talk about some mechanism which the embedding of Weighted-Sobolev spaces is compact or not. Sponsored by: Mathematical Sciences Department

PDE Seminar: Thermocapillary Controlled Rupture of Thin Liquid Sheets Wednesday, 10/26/2005, 4:00 PM-5:00 PM
Speaker: Burt Tilley (Olin College) Abstract: We consider the evolution of a thin viscous fluid sheet subject to thermocapillary effects. Using a lubrication approximation we find, for symmetric interfacial deflections, coupled evolution equations for the interfacial profile, the stream-wise component of the fluid velocity and the temperature variation along the surface. Initial temperature profiles change the initial flow field through Marangoni-induced shear stresses. These changes then lead to preferred conditions for rupture prescribed by the initial temperature distribution. We show that the time to rupture may be minimized by varying the phase difference between the initial velocity profile and the initial temperature profile. For sufficiently large temperature differences, the phase difference between the initial velocity and temperature profiles determines the rupture location.

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