HYPOCOERCIVITY AND GEOMETRIC CONDITIONS IN KINETIC THEORY.

22 January 2015
12:00
Harsha Hutridurga
Abstract
We shall discuss the problem of the 'trend to equilibrium' for a 
degenerate kinetic linear Fokker-Planck equation. The linear equation is 
assumed to be degenerate on a subregion of non-zero Lebesgue measure in the 
physical space (i.e., the equation is just a transport equation with a 
Hamiltonian structure in the subregion). We shall give necessary and 
sufficient geometric condition on the region of degeneracy which guarantees 
the exponential decay of the semigroup generated by the degenerate kinetic 
equation towards a global Maxwellian equilibrium in a weighted Hilbert 
space. The approach is strongly influenced by C. Villani's strategy of 
'Hypocoercivity' from Kinetic theory and the 'Bardos-Lebeau-Rauch' 
geometric condition from Control theory. This is a joint work with Frederic 
Herau and Clement Mouhot.
  • PDE CDT Lunchtime Seminar