Abstract
In this paper we investigate the large-time asymptotic of linearized very fast diffusion equations with and without potential confinements. These equations do not satisfy, in general, logarithmic Sobolev inequalities, but, as we show by using the `Bakry-Emery reverse approach', in the confined case they have a positive spectral gap at the eigenvalue zero. We present estimates for this spectral gap and draw conclusions on the time decay of the solution, which we show to be exponential for the problem with confinement and algebraic for the pure diffusive case. These results hold for arbitrary algebraically large diffusion speeds, if the solutions have the mass-conservation property.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
