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On the Homogenization of the Renewal Equation with Heterogeneous External Constraints

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We study the homogenization limit of the renewal equation with heterogeneous external 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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This article has been written under the auspices of the Italian National Institute of Higher Mathematics (INdAM), GNFM group. The authors are grateful to the referee for his/her comments which helped us to improve the manuscript.

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Correspondence to Étienne Bernard.

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Bernard, É., Salvarani, F. On the Homogenization of the Renewal Equation with Heterogeneous External Constraints. Acta Appl Math 187, 4 (2023).

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