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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	5811-5824
Number of pages	14
Journal	SIAM Journal on Mathematical Analysis
Volume	50
Issue number	6
DOIs	https://doi.org/10.1137/18M117981X
Publication status	Published - 1 Jan 2018
Externally published	Yes

Keywords

Generalized young measure
Growth-fragmentation equation
Measure solutions
Relative entropy
Structured population

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10.1137/18M117981X

Cite this

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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",

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T1 - Relative entropy method for measure solutions of the growth-fragmentation equation

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

U2 - 10.1137/18M117981X

DO - 10.1137/18M117981X

M3 - Article

AN - SCOPUS:85060526511

SN - 0036-1410

VL - 50

SP - 5811

EP - 5824

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 6

ER -

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

Abstract

Keywords

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