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Pré-publication, Document de travail

General Relative Entropy inequality for Cauchy problems preserving positivity in function spaces

Abstract : The Generalized Relative Entropy inequality is a ubiquitous property in linear Cauchy problems conserving positivity of the solution over time. Yet, it is currently proved on a case-by-case basis in the literature. Here, we first prove that by considering the Cauchy problems in the framework of Riesz spaces, GRE is actually a generic consequence of a Jensen-type inequality applied to a vector-valued convex function associated to the relative entropy. Next, we extend the method to the simplest case of nonlinearity, i.e. the affine case, and we show that it also implies either GRE for a subclass of convex functions either a relaxed GRE for a larger subclass, which suggests a new avenue of research for the challenge of GRE in nonlinear problems arising in population dynamics.
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Pré-publication, Document de travail
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https://hal-enpc.archives-ouvertes.fr/hal-03560418
Contributeur : Étienne Bernard Connectez-vous pour contacter le contributeur
Soumis le : lundi 7 février 2022 - 15:29:53
Dernière modification le : lundi 16 mai 2022 - 10:13:09
Archivage à long terme le : : dimanche 8 mai 2022 - 18:47:43

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GRE.pdf
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  • HAL Id : hal-03560418, version 1

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Étienne Bernard. General Relative Entropy inequality for Cauchy problems preserving positivity in function spaces. 2022. ⟨hal-03560418⟩

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