Sharp Extinction Rates for Fast Diffusion Equations on Generic Bounded Domains
METADATA ONLY
Loading...
Author / Producer
Date
2021-04
Publication Type
Journal Article
ETH Bibliography
yes
Citations
Altmetric
METADATA ONLY
Data
Rights / License
Abstract
We investigate the homogeneous Dirichlet problem for the Fast Diffusion Equation ut=Δum, posed in a smooth bounded domain Ω⊂RN, in the exponent range ms=(N−2)+/(N+2)0, and also that they approach a separate variable solution u(t,x)∼(T−t)1/(1−m)S(x), as t→T−. It has been shown recently that v(x,t)=u(t,x)(T−t)−1/(1−m) tends to S(x) as t→T−, uniformly in the relative error norm. Starting from this result, we investigate the fine asymptotic behaviour and prove sharp rates of convergence for the relative error. The proof is based on an entropy method relying on a (improved) weighted Poincaré inequality, that we show to be true on generic bounded domains. Another essential aspect of the method is the new concept of "almost orthogonality", which can be thought as a nonlinear analogous of the classical orthogonality condition needed to obtain improved Poincaré inequalities and sharp convergence rates for linear flows.
Permanent link
Publication status
published
External links
Editor
Book title
Journal / series
Communications on Pure and Applied Mathematics
Volume
74 (4)
Pages / Article No.
744 - 789
Publisher
Wiley
Event
Edition / version
Methods
Software
Geographic location
Date collected
Date created
Subject
Organisational unit
09565 - Figalli, Alessio / Figalli, Alessio
Notes
Funding
Related publications and datasets
Is new version of: