Captivity of the solution to the granular media equation

Julian Tugaut

doi:10.3934/krm.2021002

Article Contents

2021, Volume 14, Issue 2: 199-209. Doi: 10.3934/krm.2021002

This issue Previous Article Next Article Diffusion limit of the Vlasov-Poisson-Boltzmann system

Captivity of the solution to the granular media equation

Julian Tugaut^,

Univ Lyon, Université Jean Monnet, CNRS UMR 5208, Institut Camille Jordan, Maison de l'Université, 10 rue Tréfilerie, CS 82301, 42023 Saint-Átienne Cedex 2, France

^* Corresponding author: Julian Tugaut
^* Corresponding author: Julian Tugaut

Received: May 31, 2020

Revised: September 30, 2020

Early access: December 2020

Published: April 2021

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Abstract

The goal of the current paper is to provide assumptions under which the limiting probability of the granular media equation is known when there are several stable states. Indeed, it has been proved in our previous works [17,18] that there is convergence. However, very few is known about the limiting probability, even with a small diffusion coefficient.

Keywords:

Granular media equation,
Self-stabilizing diffusion,
Non uniqueness of the invariant probabilities,
Limiting probability.

Mathematics Subject Classification: Primary: 35K55, 60J60; Secondary: 26D10, 60E15, 60F10.

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References

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