| Issue |
ESAIM: ProcS
Volume 62, 2018
CIMPA School on Mathematical Models in Biology and Medicine
|
|
|---|---|---|
| Page(s) | 68 - 78 | |
| DOI | https://doi.org/10.1051/proc/201862186206 | |
| Published online | 17 October 2018 | |
Measure Solutions To The Conservative Renewal Equation★
Laboratoire de Mathématiques de Versailles, UVSQ, CNRS, Université Paris-Saclay, 45 Avenue des États-Unis, 78035 Versailles cedex, France;
*
e-mail: pierre.gabriel@uvsq.fr
We prove the existence and uniqueness of measure solutions to the conservative renewal equation and analyze their long time behavior. The solutions are built by using a duality approach. This construction is well suited to apply the Doeblin’s argument which ensures the exponential relaxation of the solutions to the equilibrium.
© EDP Sciences, SMAI 2018
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