Weighted ultrafast diffusion equations: from well-posedness to long-time behaviour
Analysis of PDEs
2019-01-30 v2
Abstract
In this paper we devote our attention to a class of weighted ultrafast diffusion equations arising from the problem of quantisation for probability measures. These equations have a natural gradient flow structure in the space of probability measures endowed with the quadratic Wasserstein distance. Exploiting this structure, in particular through the so-called JKO scheme, we introduce a notion of weak solutions, prove existence, uniqueness, BV and H^1 estimates, L^1 weighted contractivity, Harnack inequalities, and exponential convergence to a steady state.
Cite
@article{arxiv.1808.07743,
title = {Weighted ultrafast diffusion equations: from well-posedness to long-time behaviour},
author = {Mikaela Iacobelli and Francesco Patacchini and Filippo Santambrogio},
journal= {arXiv preprint arXiv:1808.07743},
year = {2019}
}