Relative entropy method for measure solutions of the growth-fragmentation equation

Tomasz Dȩbiec; Marie Doumic; Piotr Gwiazda; Emil Wiedemann

doi:10.1137/18M117981X

Relative entropy method for measure solutions of the growth-fragmentation equation

Tomasz Dȩbiec
, Marie Doumic
, Piotr Gwiazda
, Emil Wiedemann

University of Warsaw
INRIA Institut National de Recherche en Informatique et en Automatique
University of Vienna
Institute of Mathematics of the Polish Academy of Sciences
University of Ulm

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

The aim of this study is to generalize recent results of the two last authors on entropy methods for measure solutions of the renewal equation to other classes of structured population problems. Specifically, we develop a generalized relative entropy inequality for the growth-fragmentation equation and prove asymptotic convergence to a steady-state solution, even when the initial datum is only a nonnegative measure.

langue originale	Anglais
Pages (de - à)	5811-5824
Nombre de pages	14
journal	SIAM Journal on Mathematical Analysis
Volume	50
Numéro de publication	6
Les DOIs	https://doi.org/10.1137/18M117981X
état	Publié - 1 janv. 2018
Modification externe	Oui

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10.1137/18M117981X

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title = "Relative entropy method for measure solutions of the growth-fragmentation equation",

abstract = "The aim of this study is to generalize recent results of the two last authors on entropy methods for measure solutions of the renewal equation to other classes of structured population problems. Specifically, we develop a generalized relative entropy inequality for the growth-fragmentation equation and prove asymptotic convergence to a steady-state solution, even when the initial datum is only a nonnegative measure.",

keywords = "Generalized young measure, Growth-fragmentation equation, Measure solutions, Relative entropy, Structured population",

author = "Tomasz Dȩbiec and Marie Doumic and Piotr Gwiazda and Emil Wiedemann",

note = "Publisher Copyright: {\textcopyright} 2018 Society for Industrial and Applied Mathematics.",

year = "2018",

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doi = "10.1137/18M117981X",

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AU - Dȩbiec, Tomasz

AU - Doumic, Marie

AU - Gwiazda, Piotr

AU - Wiedemann, Emil

PY - 2018/1/1

Y1 - 2018/1/1

N2 - The aim of this study is to generalize recent results of the two last authors on entropy methods for measure solutions of the renewal equation to other classes of structured population problems. Specifically, we develop a generalized relative entropy inequality for the growth-fragmentation equation and prove asymptotic convergence to a steady-state solution, even when the initial datum is only a nonnegative measure.

AB - The aim of this study is to generalize recent results of the two last authors on entropy methods for measure solutions of the renewal equation to other classes of structured population problems. Specifically, we develop a generalized relative entropy inequality for the growth-fragmentation equation and prove asymptotic convergence to a steady-state solution, even when the initial datum is only a nonnegative measure.

KW - Generalized young measure

KW - Growth-fragmentation equation

KW - Measure solutions

KW - Relative entropy

KW - Structured population

UR - https://www.scopus.com/pages/publications/85060526511

U2 - 10.1137/18M117981X

DO - 10.1137/18M117981X

M3 - Article

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VL - 50

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JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

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ER -

Relative entropy method for measure solutions of the growth-fragmentation equation

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