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arXiv · 1808.07743

Weighted ultrafast diffusion equations: from well-posedness to long-time behaviour

Mikaela Iacobelli·Francesco Patacchini·Filippo Santambrogio
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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.

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Mikaela Iacobelli, Francesco Patacchini, Filippo Santambrogio. 2018-10-24. Weighted ultrafast diffusion equations: from well-posedness to long-time behaviour. https://doi.org/10.1007/s00205-018-01341-w

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