Singular Perturbation Problems in Periodic Domains

Matteo Dalla Riva, Massimo Lanza de Cristoforis and Paolo Musolino
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Matteo Dalla Riva: The University of Tulsa, College of Engineering and Natural Science
Massimo Lanza de Cristoforis: Università degli Studi di Padova, Dipartimento di Matematica
Paolo Musolino: Università Ca’ Foscari Venezia, Dipartimento di Scienze Molecolari e Nanosistemi

Chapter Chapter 13 in Singularly Perturbed Boundary Value Problems, 2021, pp 513-614 from Springer

Abstract: Abstract In this chapter, we study the asymptotic behavior of the solutions of singularly perturbed boundary value problems in periodic domains. We introduce the domain 𝕊 [ Ω p , 𝜖 ] − $${\mathbb {S}} [\varOmega _{p,\epsilon }]^-$$ obtained by removing from the Euclidean space a periodic set of inclusions, each of them of a size controlled by a positive parameter 𝜖. Then, for each positive and sufficiently small 𝜖, we consider a boundary value problem in 𝕊 [ Ω p , 𝜖 ] − $${\mathbb {S}} [\varOmega _{p,\epsilon }]^-$$ or a transmission problem in the pair of domains consisting of 𝕊 [ Ω p , 𝜖 ] − $${\mathbb {S}} [\varOmega _{p,\epsilon }]^-$$ and its complementary set 𝕊 [ Ω p , 𝜖 ] $${\mathbb {S}} [\varOmega _{p,\epsilon }]$$ , and we analyze the behavior of the solution as the parameter 𝜖 tends to 𝜖 = 0.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-76259-9_13

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DOI: 10.1007/978-3-030-76259-9_13

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