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

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.
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Submitted on : Tuesday, April 10, 2018 - 3:31:53 PM
Last modification on : Friday, July 12, 2019 - 3:19:56 PM

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  • HAL Id : hal-01762974, version 1
  • ARXIV : 1804.03538

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

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