Weighted Ultrafast Diffusion Equations: From Well-Posedness to Long-Time Behaviour View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2019-06

AUTHORS

Mikaela Iacobelli, Francesco S. Patacchini, Filippo Santambrogio

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 H1 estimates, L1 weighted contractivity, Harnack inequalities, and exponential convergence to a steady state. More... »

PAGES

1165-1206

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00205-018-01341-w

DOI

http://dx.doi.org/10.1007/s00205-018-01341-w

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1110752304


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50 schema:description 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.
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