Communications in Mathematical Sciences

Volume 15 (2017)

Number 2

Generalized entropy method for the renewal equation with measure data

Pages: 577 – 586

(Fast Communication)



Piotr Gwiazda (Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland; and Institute of Applied Mathematics and Mechanics, University of Warsaw, Poland)

Emil Wiedemann (Institute for Applied Mathematics, Leibniz Universität, Hannover, Germany)


We study the long-time asymptotics for the so-called McKendrick–Von Foerster or renewal equation, a simple model frequently considered in structured population dynamics. In contrast to previous works, we can admit a bounded measure as initial data. To this end, we apply techniques from the calculus of variations that have not been employed previously in this context. We demonstrate how the generalized relative entropy method can be refined in the Radon measure framework.


structured population model, positive Radon measures, generalized relative entropy methods, measure-valued solutions, concentration measure

2010 Mathematics Subject Classification

Primary 35R06. Secondary 35B40, 35F10, 35Q92, 92D25.

Published 21 February 2017