On the homogenization of a Signorini-type problem in a domain with inclusions
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917699748102144 |
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| author | Monsurrò, Sara Perugia, Carmen Raimondi, Federica |
| author_facet | Monsurrò, Sara Perugia, Carmen Raimondi, Federica |
| contents | 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 $γ$. 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 $γ$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_14344 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the homogenization of a Signorini-type problem in a domain with inclusions Monsurrò, Sara Perugia, Carmen Raimondi, Federica Analysis of PDEs 35B27, 35J25, 35J20, 35J60, 35R35 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 $γ$. 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 $γ$. |
| title | On the homogenization of a Signorini-type problem in a domain with inclusions |
| topic | Analysis of PDEs 35B27, 35J25, 35J20, 35J60, 35R35 |
| url | https://arxiv.org/abs/2406.14344 |