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Summary: Improved entropy decay estimates for the
heat equation
A. Arnold a
, J. A. Carrillo b
, C. Klapproth c
aInstitut f¨ur Analysis und Scientific Computing, E101, Technische Universit¨at
Wien, Wiedner Hauptstr. 8, A-1040 Wien, Austria
bInstituci´o Catalana de Recerca i Estudis Avan¸cats and Departament de
Matem`atiques, Universitat Aut`onoma de Barcelona, E-08193 Bellaterra, Spain
cZuse Institute Berlin (ZIB), Takustr. 7, D-14195 Berlin, Germany
Abstract
Improved entropy decay estimates for the heat equation are obtained by select-
ing well parametrized Gaussians. Either by mass centering or by fixing the second
moments or the covariance matrix of the solution, relative entropy towards these
Gaussians is shown to decay with better constants than classical estimates.
Key words: entropy method, heat equation, large time behavior
2000 MSC: 35K15, 35B40
1 Introduction
Describing the asymptotic behavior of diffusion and homogeneous kinetic models has
recently received a lot of attention in the partial differential equations community
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