Seminar in Applied Mathematics

Robert Pego Department of Mathematics University of Maryland Dynamics in the Classical Theory of Domain Coarsening Tuesday, April 18, 2000 3:15pm Pierce 216

Abstract:   The classical theory of domain coarsening during phase transitions in materials science involves a conservation law for the size distribution of a family of particles. Early predictions of asymptotically self-similar behavior successfully described scaling exponents but not some other features of dynamics. I will describe recent results concerning: (a) The initial value problem: We give a theory that yields existence, uniqueness and continuous dependence on initial data for arbitrary measure-valued size distributions of compact support. We use a physically natural topology given by a Wasserstein distance between size distributions. (b) Long-time behavior: This depends sensitively on the initial distribution of the largest particles in the system. Convergence to the classically predicted smooth similarity solution is impossible if the initial distribution function is comparable to any finite power of distance to the end of the support. We give a necessary criterion for convergence to any other self-similar solution. For a dense set of initial data, convergence to any self-similar solution is impossible. This is joint work with Barbara Niethammer, University of Bonn.

Coffee and refreshments will be available starting at 3:00pm. For additional information contact Patrick Miller  or Yi Li.