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

Tomasz Deͅbiec, Marie Doumic, Piotr Gwiazda, Emil Wiedemann
2018 SIAM Journal on Mathematical Analysis  
The aim of this study is to generalise 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 generalised relative entropy inequality for the growthfragmentation equation and prove asymptotic convergence to a steady-state solution, even when the initial datum is only a non-negative measure.
doi:10.1137/18m117981x fatcat:ejgtqpoqsrge7lxeye2rjcecai