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Chris Burdzy, University of Washington."On the Robin Problem in Fractal Domains" AbstractThe ``Robin problem" or the "third boundary problem" is a mathematical model for the flow of a substance (or heat) out of a domain through a semipermeable membrane. The model applies to man-made objects such as electrodes in car batteries and natural objects such as lungs. I will address the question of when the concentration of the substance (or the temperature) is bounded below by a constant over the whole domain. The solution of the analytic problem involves stochastic processes -- in particular, the argument is based in part on a very non-trivial (although old) result known as the "Ray-Knight theorem". The talk will be accessible to non-specialists and graduate students.* Joint work with Rich Bass and Zhenqing Chen. FRIDAY, September 16, 2005 |