Measure solutions to the conservative renewal equation

Pierre Gabriel (1)

1 LMV - Laboratoire de Mathématiques de Versailles

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.

Domaines: Equations aux dérivées partielles [math.AP]

Pierre Gabriel. Measure solutions to the conservative renewal equation. 2017. ⟨hal-01500471v1⟩