We extend the existing theory on large-time asymptotics for convection-diffusion equations, based on the entropy-entropy dissipation approach, to certain fast diffusion equations with uniformly convex confinement potential and finite-mass but infinite-entropy equilibrium solutions. We prove existence of a mass preserving solution of the Cauchy problem and we show exponential convergence, as t → ∞, at a precise rate to the corresponding equilibrium solution in the L1 norm. As by-product we also derive corresponding generalized Sobolev inequalities.
ASJC Scopus subject areas
- Applied Mathematics