Anomalous diffusion phenomena: A kinetic approach

Mellet, Antoine

doi:10.5802/slsedp.72

Séminaire Laurent Schwartz — EDP Et Applications

2015

DOI: 10.5802/slsedp.72

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Anomalous diffusion phenomena: A kinetic approach

Antoine Mellet¹

Abstract: Anomalous diffusion phenomena: A kinetic approachSéminaire Laurent Schwartz -EDP et applications (2014-2015 AbstractIn this talk, we review some aspects of the derivation of fractional diffusion equations from kinetic equations and in particular some applications to the description of anomalous energy transport in FPU chains. This is based on joint works with N. Ben Abdallah, L. Cesbron, S. Merino, S. Mischler, C. Mouhot and M. Puel

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References 30 publications

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Anomalous diffusion limit for a kinetic equation with a thermostatted interface

Bogdan,

Komorowski,

Marino

2023

Probab. Theory Relat. Fields

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We consider the limit of solutions of scaled linear kinetic equations with a reflection-transmission-killing condition at the interface. Both the coefficient describing the probability of killing and the scattering kernel degenerate. We prove that the long-time, large-space limit is the unique solution of a version of the fractional in space heat equation that corresponds to the Kolmogorov equation for a symmetric stable process, which is reflected, or transmitted while crossing the interface and is killed upon the first hitting of the interface. The results of the paper are related to the work in Komorowski et al. (Ann Prob 48:2290–2322, 2020), where the case of a non-degenerate probability of killing has been considered.

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Anomalous diffusion limit for a kinetic equation with a thermostatted interface

Bogdan,

Komorowski,

Marino

2023

Probab. Theory Relat. Fields

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Fractional diffusion limit for a kinetic equation with an interface

Komorowski¹,

Olla²,

Ryzhik³

2020

Ann. Probab.

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Anomalous diffusion phenomena: A kinetic approach

Cited by 2 publications

References 30 publications

Anomalous diffusion limit for a kinetic equation with a thermostatted interface

Anomalous diffusion limit for a kinetic equation with a thermostatted interface

Fractional diffusion limit for a kinetic equation with an interface

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