Microscopic behavior of the solutions of a transmission problem for the Helmholtz equation: a functional analytic approach

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dc.authorid0000-0001-6484-2731en_US
dc.contributor.authorAkyel, Tuğba
dc.contributor.authorLanza de Cristoforis, Massimo
dc.date.accessioned2024-07-12T20:58:04Z
dc.date.available2024-07-12T20:58:04Z
dc.date.issued2022en_US
dc.departmentFakülteler, Mühendislik ve Doğa Bilimleri Fakültesi, Bilgisayar Mühendisliği Bölümüen_US
dc.description.abstractLet Omega(i), Omega(o) be bounded open connected subsets of R-n that contain the origin. Let Omega(epsilon) equivalent to Omega(o) \ c (Omega) over bar (i) for small epsilon > 0. Then we consider a linear transmission problem for the Helmholtz equation in the pair of domains epsilon Omega(i) and Omega(epsilon) with Neumann boundary conditions on partial derivative Omega(o). Under appropriate conditions on the wave numbers in epsilon Omega(i) and Omega(epsilon) and on the parameters involved in the transmission conditions on epsilon partial derivative Omega(i), the transmission problem has a unique solution (u(i)(epsilon, .); u(o) (epsilon, .)) for small values of epsilon > 0. Here u(i)(epsilon, .) and u(o) (epsilon, .) solve the Helmholtz equation in epsilon Omega(i) and Omega(epsilon), respectively. Then we prove that if xi is an element of(Omega(i)) over bar and xi is an element of R-n\Omega(i) then the rescaled solutions u(i) (epsilon, epsilon xi) and u(o) (epsilon, epsilon xi) can be expanded into a convergent power expansion of epsilon, kappa(n) is an element of log epsilon, delta(2,n) log(-1) epsilon, kappa(n) is an element of log(2) epsilon for epsilon small enough. Here kappa(n) = 1 if n is even and kappa(n) = 0 if n is odd and delta(2,2) equivalent to 1 and delta(2,n) equivalent to 0 if n >= 3.en_US
dc.identifier.citationAkyel, T. and Lanza de Cristoforis, M (2022). Microscopic behavior of the solutions of a transmission problem for the Helmholtz equation: a functional analytic approach. Stud. Univ. Babeş-Bolyai Math., 67(10), p.383-402.en_US
dc.identifier.doi10.24193/subbmath.2022.2.14
dc.identifier.endpage402en_US
dc.identifier.issue10en_US
dc.identifier.scopus2-s2.0-85132337391en_US
dc.identifier.startpage383en_US
dc.identifier.urihttps://doi.prg/10.24193/subbmath.2022.2.14
dc.identifier.urihttps://hdl.handle.net/20.500.12415/3134
dc.identifier.volume67en_US
dc.identifier.wosWOS:000810067300015en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoenen_US
dc.publisherStud. Univ. Babe¸s-Bolyai Math.en_US
dc.relation.ispartofStud. Univ. Babeş-Bolyai Math.en_US
dc.relation.publicationcategoryUluslararası Hakemli Dergide Makale - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.snmzKY03448
dc.subjectHelmholtz equationen_US
dc.subjectMicroscopic behavioren_US
dc.subjectReal analytic continuationen_US
dc.subjectSingularly perturbed domainen_US
dc.subjectTransmission problemen_US
dc.titleMicroscopic behavior of the solutions of a transmission problem for the Helmholtz equation: a functional analytic approachen_US
dc.typeArticle
dspace.entity.typePublication

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