ON THE HOMOGENIZATION OF THE RENEWAL EQUATION WITH HETEROGENEOUS EXTERNAL CONSTRAINTS

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 renewal equation with heterogeneous ex- ternal constraints by means of the two-scale convergence theory. We prove that the homogenized limit satisfies an equation involving non-local terms, which are the consequence of the oscillations in the birth and death terms. We have moreover shown that the numerical approximation of the homogenized equation via the two-scale limit gives an alternative way for the numerical study of the solution of the limiting problem.

Mots clés: Renewal equation; homogenization; two-scale convergence

Domaines: Mathématiques [math]

Étienne Bernard, Francesco Salvarani. ON THE HOMOGENIZATION OF THE RENEWAL EQUATION WITH HETEROGENEOUS EXTERNAL CONSTRAINTS. 2023. ⟨hal-04039996v2⟩