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WROCŁAW UNIVERSITY
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TECHNOLOGY

Contents of PMS, Vol. 39, Fasc. 5,
pages 75 - 84
DOI: 10.19195/0208-4147.39.1.5
 

FINITENESS OF ENTROPY FOR GRANULAR MEDIA EQUATIONS

Julian Tugaut

Abstract: The current work deals with the granular media equation whose probabilistic interpretation is the McKean–Vlasov diffusion. It is well known that the Laplacian provides a regularization of the solution. Indeed, for any t > 0 , the solution is absolutely continuous with respect to the Lebesgue measure. It has also been proved that all the moments are bounded for positive t . However, the finiteness of the entropy of the solution is a new result which will be presented here.

2000 AMS Mathematics Subject Classification: Primary: 35K55; Secondary: 60J60, 60E15.

Keywords and phrases: Granular media equation, McKean–Vlasov diffusion, Wasserstein distance, functional inequalities, entropy.

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