ON THE HOMOGENIZATION OF THE RENEWAL EQUATION WITH HETEROGENEOUS EXTERNAL CONSTRAINTS - École des Ponts ParisTech Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

ON THE HOMOGENIZATION OF THE RENEWAL EQUATION WITH HETEROGENEOUS EXTERNAL CONSTRAINTS

Résumé

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.
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Dates et versions

hal-04039996 , version 1 (21-03-2023)
hal-04039996 , version 2 (23-08-2023)

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