Exotic Distributions as Weak Solutions to Kinetic Equations
speaker: Bruce Boghosian (Tufts University)abstract: It is well known that certain kinetic equations, including Fokker-Planck equations derived in the grazing-collision limit of Boltzmann equations, can have generalized distributions as weak solutions. These may appear either as initial conditions, time-asymptotic states, or singularities that manifest themselves in finite time. The most well-known of these generalized distributions is the Dirac delta, but in recent years it has become clear that there are others of more exotic form, and they have physical significance ranging from conservation of heat energy in infinite domains, to wealth distribution in the presence of oligarchy, to the energy distribution of runaway electrons. The mathematical tools used to understand such exotic distributions range from Sobolev-Schwarz distribution theory to nonstandard analysis, to measure theory. This talk will begin with an introduction to such exotic generalized distributions at a level accessible to an advanced undergraduate, and gradually ramp up to some of the unsolved problems of the field. (This is joint work with Adrian Devitt-Lee, David Cohen, and Sauro Succi.)
timetable:
Tue 29 Nov, 16:00 - 17:00, Sala Azzurra
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