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Article: Asymptotic analysis for elliptic equations with small perturbations on domains in high-contrast medium

TitleAsymptotic analysis for elliptic equations with small perturbations on domains in high-contrast medium
Authors
KeywordsAsymptotic analysis
interface problem
high-contrast ratio
two-parameter expansion
Issue Date2020
PublisherIOS Press. The Journal's web site is located at https://www.iospress.nl/journal/asymptotic-analysis/
Citation
Asymptotic Analysis, 2020, v. 119 n. 3-4, p. 153-198 How to Cite?
AbstractWe provide a comprehensive study on the asymptotic solutions of an interface problem corresponding to an elliptic partial differential equation with Dirichlet boundary condition and transmission condition, subject to the small geometric perturbation and/or the high contrast ratio of the conductivity. All asymptotic terms can be solved in the unperturbed reference domains, which significantly reduces computations in practice, especially for random perturbations. Our setting is quite general and allows two types of elliptic problems: the perturbation of the domain boundary where the Dirchlet condition is imposed and the perturbation of the interface where the transmission condition is imposed. As the perturbation size and the ratio of the conductivities tends to zero, the two-parameter asymptotic expansions on the reference domain are derived to any order after the single parameter expansions are solved beforehand. The results suggest the emergence of the Neumann or Robin boundary condition, depending on the relation of the two asymptotic parameters. Our method is the classic asymptotic analysis techniques but in a new unified approach to both problems.
Persistent Identifierhttp://hdl.handle.net/10722/278191
ISSN
2023 Impact Factor: 1.1
2023 SCImago Journal Rankings: 0.789
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorChen, J-
dc.contributor.authorLin, L-
dc.contributor.authorZhang, Z-
dc.contributor.authorZhou, X-
dc.date.accessioned2019-10-04T08:09:14Z-
dc.date.available2019-10-04T08:09:14Z-
dc.date.issued2020-
dc.identifier.citationAsymptotic Analysis, 2020, v. 119 n. 3-4, p. 153-198-
dc.identifier.issn0921-7134-
dc.identifier.urihttp://hdl.handle.net/10722/278191-
dc.description.abstractWe provide a comprehensive study on the asymptotic solutions of an interface problem corresponding to an elliptic partial differential equation with Dirichlet boundary condition and transmission condition, subject to the small geometric perturbation and/or the high contrast ratio of the conductivity. All asymptotic terms can be solved in the unperturbed reference domains, which significantly reduces computations in practice, especially for random perturbations. Our setting is quite general and allows two types of elliptic problems: the perturbation of the domain boundary where the Dirchlet condition is imposed and the perturbation of the interface where the transmission condition is imposed. As the perturbation size and the ratio of the conductivities tends to zero, the two-parameter asymptotic expansions on the reference domain are derived to any order after the single parameter expansions are solved beforehand. The results suggest the emergence of the Neumann or Robin boundary condition, depending on the relation of the two asymptotic parameters. Our method is the classic asymptotic analysis techniques but in a new unified approach to both problems.-
dc.languageeng-
dc.publisherIOS Press. The Journal's web site is located at https://www.iospress.nl/journal/asymptotic-analysis/-
dc.relation.ispartofAsymptotic Analysis-
dc.subjectAsymptotic analysis-
dc.subjectinterface problem-
dc.subjecthigh-contrast ratio-
dc.subjecttwo-parameter expansion-
dc.titleAsymptotic analysis for elliptic equations with small perturbations on domains in high-contrast medium-
dc.typeArticle-
dc.identifier.emailZhang, Z: zhangzw@hku.hk-
dc.identifier.authorityZhang, Z=rp02087-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.3233/ASY-191571-
dc.identifier.scopuseid_2-s2.0-85093839856-
dc.identifier.hkuros306346-
dc.identifier.volume119-
dc.identifier.issue3-4-
dc.identifier.spage153-
dc.identifier.epage198-
dc.identifier.isiWOS:000577857100001-
dc.publisher.placeNetherlands-
dc.identifier.issnl0921-7134-

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