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Open AccessArticle10.1478/aapp.91s1a18

Lyapunov functionals for the heat equation and sharp inequalities

Giuseppe Toscani-2013-01-29-University of Messina University Library System (University of Messina)
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TL;DRAbstract

The heat equation represents a powerful instrument to obtain a number of mathematical inequalities in sharp form.This maybe 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.

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The heat equation represents a powerful instrument to obtain a number of mathematical inequalities in sharp form.This maybe 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.

Keywords

Connection (principal bundle)Heat equationBoltzmann equationMathematicsProperty (philosophy)InequalityLyapunov functionKinetic theory

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