On the homogenization of a Signorini-type problem in a domain with inclusions

In this paper we investigate the effect of a Signorini-type interface condition on the asymptotic behaviour, as $\varepsilon$ tends to zero, of problems posed in $\varepsilon$-periodic domains with inclusions. The Signorini-type condition is expressed in terms of two complementary equalities involvi...

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Bibliographic Details
Main Authors Monsurrò, Sara, Perugia, Carmen, Raimondi, Federica
Format Journal Article
LanguageEnglish
Published 20.06.2024
Subjects
Mathematics - Analysis of PDEs
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Summary:In this paper we investigate the effect of a Signorini-type interface condition on the asymptotic behaviour, as $\varepsilon$ tends to zero, of problems posed in $\varepsilon$-periodic domains with inclusions. The Signorini-type condition is expressed in terms of two complementary equalities involving the jump of the solution on the interface and its conormal derivative via a parameter $\gamma$. Our problem models the heat exchange in a medium hosting an $\varepsilon$-periodic array of thermal conductors in presence of impurities distributed on some regions of the interface. Different limit problems are obtained according to different values of $\gamma$.
DOI:10.48550/arxiv.2406.14344