Weighted ultrafast diffusion equations : from well-posedness to long-time behaviour
| Autor: | Filippo Santambrogio, Francesco S. Patacchini, Mikaela Iacobelli |
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| Přispěvatelé: | Durham University, Carnegie Mellon University [Pittsburgh] (CMU), Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2019 |
| Předmět: |
Mechanical Engineering
010102 general mathematics Complex system Structure (category theory) Space (mathematics) 01 natural sciences 010101 applied mathematics Mathematics - Analysis of PDEs Mathematics (miscellaneous) Quadratic equation Flow (mathematics) FOS: Mathematics Applied mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Uniqueness 0101 mathematics Diffusion (business) Analysis Analysis of PDEs (math.AP) Probability measure Mathematics |
| Zdroj: | Archive for rational mechanics and analysis, 2019, Vol.232(3), pp.1165-1206 [Peer Reviewed Journal] Archive for Rational Mechanics and Analysis, 232 (3) |
| ISSN: | 0003-9527 1432-0673 |
| Popis: | 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 H1 estimates, L1 weighted contractivity, Harnack inequalities, and exponential convergence to a steady state. Archive for Rational Mechanics and Analysis, 232 (3) ISSN:0003-9527 ISSN:1432-0673 |
| Databáze: | OpenAIRE |
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