11h10 Wednesday Aug 13 

Fields Analysis Working Group at Fields Institute

Speaker: Jochen Denzler (University of Tennessee)


Title: Spectral theory and convergence rates for the fast diffusion equation in weighted 
Hoelder spaces

Abstract: For the fast diffusion equation in the mass preserving parameter range, we
obtain sharp asymptotic convergence  rates to the Barenblatt solution
with respect to the relative L-infinity norm from spectral gaps by
establishing a nonlinear differentiable semiflow in Hoelder spaces on a Riemannian
manifold called the cigar manifold. On this manifold, the equation becomes 
uniformly parabolic. It is possible to obtain faster rates than O(1/t) when the
reference Barenblatt solution is appropriately scaled. To this end, the
interplay between weights in the function space, the spectrum of the
linearized operator and growth of its (formal) eigenfunctions needs to be
investigated carefully, leading to estimates in appropriately weighted
relative L-infinity norms.

(joint work with Herbert Koch and Robert McCann)