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
3 WPI - Wolfgang Pauli Institute
4 Institute of Mathematics [Warsaw]
5 IFAM - Institut für Angewandte Mathematik [Hannover]

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.

Mots clés: Generalised Young measure; Structured population; Relative entropy; Growth-fragmentation equation; Measure solutions

Domaines: Equations aux dérivées partielles [math.AP]

Tomasz Dębiec, Marie Doumic, Piotr Gwiazda, Emil Wiedemann. Relative Entropy Method for Measure Solutions of the Growth-Fragmentation Equation. SIAM Journal on Applied Mathematics, 2018, 50 (6), pp.5811-5824. ⟨hal-01762974⟩