Measure solutions to the conservative renewal equation

Abstract

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.

Cited by in corpus (12)

• Ergodic behavior of non-conservative semigroups via generalized Doeblin's conditions
• A non-conservative Harris ergodic theorem
• Asymptotic behaviour of neuron population models structured by elapsed-time
• Spectral gap for the growth-fragmentation equation via Harris's Theorem
• Periodic asymptotic dynamics of the measure solutions to an equal mitosis equation
• The mean-field equation of a leaky integrate-and-fire neural network: measure solutions and steady states
• A multiple time renewal equation for neural assemblies with elapsed time model
• On quantitative hypocoercivity estimates based on Harris-type theorems
• Exponential ergodicity of a degenerate age-size piecewise deterministic process
• On the Krein-Rutman theorem and beyond
• On the asymptotic behaviour of a run and tumble equation for bacterial chemotaxis
• Asymptotic behaviour of a structured population model on a space of measures