Relative Entropy Method for Measure Solutions of the Growth-Fragmentation Equation

Tomasz Dębiec; Marie Doumic; Piotr Gwiazda; Emil Wiedemann

Journal articles

Relative Entropy Method for Measure Solutions of the Growth-Fragmentation Equation

Tomasz Dębiec ¹ Marie Doumic ^{2, 3} Piotr Gwiazda ⁴ Emil Wiedemann ⁵

1 IMSM - Institute of Applied Mathematics [Warsaw]

2 MAMBA - Modelling and Analysis for Medical and Biological Applications

Inria de Paris, LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

3 WPI - Wolfgang Pauli Institute

4 Institute of Mathematics [Warsaw]

5 IFAM - Institut für Angewandte Mathematik [Hannover]

Abstract : The aim of this study is to generalise recent results of the two last authors on en-tropy methods for measure solutions of the renewal equation to other classes of structured population problems. Specifically, we develop a generalised 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 non-negative measure.

Keywords : Relative entropy Structured population Generalised Young measure Measure solutions Growth-fragmentation equation

Document type :

Journal articles

Domain :

Mathematics [math] / Analysis of PDEs [math.AP]

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https://hal.inria.fr/hal-01762974
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Submitted on : Tuesday, April 10, 2018 - 3:31:53 PM
Last modification on : Monday, June 8, 2020 - 10:52:02 AM

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Relative Entropy Method for Measure Solutions of the Growth-Fragmentation Equation

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438

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