Thin Films Seminar
Wednesday, April 23, 2003, 12:00pm, 054 Physics
Michael Shearer (North Carolina State University, Department of Mathematics)
Kinetics and Nucleation for Scalar Conservation Laws Related to the Flow of Thin Liquid Films
Abstract:- Recent simulations of thin film equations suggest the need for a kinetic
relation and nucleation condition to describe the structure of waves for the
underlying hyperbolic conservation law. Using front tracking, we establish
the existence of solutions of the Cauchy problem. More interestingly, we
find that for a range of choices of upstream and downstream heights, the
conservation law has two attractors, i.e., two long-time wave structures.
The corresponding domains of attraction depend on the internal structure of
the initial data in a way that is more subtle than expected. This is joint
work with Philippe LeFloch.
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