ON THE HOMOGENEIZATION OF THE RENEWAL EQUATION

Étienne Bernard (1) , Francesco Salvarani (2, 3)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 Dipartimento di matematica F. Casorati
3 PULV - Pôle Universitaire Léonard de Vinci

We study the homogenization limit of the space-heterogeneous renewal equation by means of the two-scale convergence theory. We prove that the homogenized limit satisfies an equation involving nonlocal terms, which are the consequence of the oscillations in the birth and death terms. The numerical approximation of the homogenized equation via the two-scale limit can give an alternative way for the numerical study of the solution of the limiting problem.

Keywords: Renewal equation; homogenization; two-scale convergence

Domains: Mathematics [math]

Étienne Bernard, Francesco Salvarani. ON THE HOMOGENEIZATION OF THE RENEWAL EQUATION. 2023. ⟨hal-04039996⟩