Lyapunov functionals for the heat equation and sharp inequalities

Lyapunov functionals for the heat equation and sharp inequalities

The heat equation represents a powerful instrument to obtain a number of mathematical inequalities in sharp form. This may be not so well-known property goes back more or less to half a century ago, when independently from each others, researchers from information theory [22, 6] and kinetic theory [...

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Main Author: Giuseppe Toscani
Format: Article
Language:English
Published: Accademia Peloritana dei Pericolanti 2013-01-01
Series:Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali
Online Access:http://dx.doi.org/10.1478/AAPP.91S1A18
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spelling doaj-a1cfb83c9055412aac8b91e261726a7a2020-11-24T21:38:19ZengAccademia Peloritana dei PericolantiAtti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali0365-03591825-12422013-01-0191S1A1810.1478/AAPP.91S1A18Lyapunov functionals for the heat equation and sharp inequalitiesGiuseppe ToscaniThe heat equation represents a powerful instrument to obtain a number of mathematical inequalities in sharp form. This may be not so well-known property goes back more or less to half a century ago, when independently from each others, researchers from information theory [22, 6] and kinetic theory [20] established a useful connection between Boltzmann’s H-functional and Fisher information exactly by means of the solution to the heat equation. In this note, we briefly discuss these original ideas, together with some new application.http://dx.doi.org/10.1478/AAPP.91S1A18
collection DOAJ
language English
format Article
sources DOAJ
author Giuseppe Toscani
spellingShingle Giuseppe Toscani
Lyapunov functionals for the heat equation and sharp inequalities
Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali
author_facet Giuseppe Toscani
author_sort Giuseppe Toscani
title Lyapunov functionals for the heat equation and sharp inequalities
title_short Lyapunov functionals for the heat equation and sharp inequalities
title_full Lyapunov functionals for the heat equation and sharp inequalities
title_fullStr Lyapunov functionals for the heat equation and sharp inequalities
title_full_unstemmed Lyapunov functionals for the heat equation and sharp inequalities
title_sort lyapunov functionals for the heat equation and sharp inequalities
publisher Accademia Peloritana dei Pericolanti
series Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali
issn 0365-0359
1825-1242
publishDate 2013-01-01
description The heat equation represents a powerful instrument to obtain a number of mathematical inequalities in sharp form. This may be not so well-known property goes back more or less to half a century ago, when independently from each others, researchers from information theory [22, 6] and kinetic theory [20] established a useful connection between Boltzmann’s H-functional and Fisher information exactly by means of the solution to the heat equation. In this note, we briefly discuss these original ideas, together with some new application.
url http://dx.doi.org/10.1478/AAPP.91S1A18
work_keys_str_mv AT giuseppetoscani lyapunovfunctionalsfortheheatequationandsharpinequalities
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