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

Sara Monsurrò; Carmen Perugia; Federica Raimondi

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arXiv · 2406.14344

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

Sara Monsurrò·Carmen Perugia·Federica Raimondi

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Abstract

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 $\gamma$.

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Sara Monsurrò, Carmen Perugia, Federica Raimondi. 2024-06-20. On the homogenization of a Signorini-type problem in a domain with inclusions. https://arxiv.org/abs/2406.14344

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