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SUMMARY:Can spectral gap form in soft potentials? - Renjun Duan (Chinese U
 niversity of Hong Kong)
DTSTART:20220113T143000Z
DTEND:20220113T153000Z
UID:TALK166651@talks.cam.ac.uk
DESCRIPTION:In the talk I will consider the spectral gap for the linearize
 d Boltzmann or Landau equation with soft potentials. It is known that the 
 corresponding collision operators admit only the degenerated spectral gap.
  We rather prove the formation of spectral gap in the spatially inhomogene
 ous setting where the space domain is bounded with an inflow boundary cond
 ition. The key strategy is to introduce a new Hilbert space with an expone
 ntial weight function that involves the inner product of space and velocit
 y variables and also has the strictly positive upper and lower bounds. The
  action of the transport operator on such space-velocity dependent weight 
 function induces an extra non-degenerate relaxation dissipation in large v
 elocity that can be employed to compensate the degenerate spectral gap and
  hence give the exponential decay for solutions in contrast with the sub-e
 xponential decay in either the spatially homogeneous case or the case of t
 orus domain. The result reveals a new insight of hypocoercivity for kineti
 c equations with soft potentials in the specified situation.
LOCATION:Seminar Room 1\, Newton Institute
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