General Relative Entropy inequality for Cauchy problems preserving positivity in function spaces - École des Ponts ParisTech Access content directly
Preprints, Working Papers, ... Year :

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.
Fichier principal
Vignette du fichier
GRE.pdf (270.26 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03560418 , version 1 (07-02-2022)
hal-03560418 , version 2 (24-06-2022)

Identifiers

  • HAL Id : hal-03560418 , version 1

Cite

Étienne Bernard. General Relative Entropy inequality for Cauchy problems preserving positivity in function spaces. 2022. ⟨hal-03560418v1⟩
31 View
31 Download

Share

Gmail Facebook Twitter LinkedIn More