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

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dc.authoridLanza de Cristoforis, Massimo/0000-0001-6886-4647en_US
dc.contributor.authorAkyel, Tuğba
dc.contributor.authorLanza de Cristoforis, Massimo
dc.date.accessioned2024-07-12T21:37:42Z
dc.date.available2024-07-12T21:37:42Z
dc.date.issued2022en_US
dc.department[Belirlenecek]en_US
dc.description.abstractLet omega(i), omega(o) be bounded open connected subsets of Double-struck capital Rn that contain the origin. Let omega(epsilon)equivalent to omega o\epsilon omega 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 differential 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 differential omega(i), the transmission problem has a unique solution (u(i)(epsilon, center dot), u(o)(epsilon, center dot)) for small values of epsilon > 0. Here, u(i)(epsilon, center dot) and u(o)(epsilon, center dot) solve the Helmholtz equation in epsilon omega(i) and omega(epsilon), respectively. Then, we prove that if x is an element of omega(o) \ {0}, then u(o)(epsilon, x) can be expanded into a convergent power expansion of epsilon, kappa n epsilon log epsilon,delta 2,nlog-1 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.description.sponsorshipIstituto Nazionale di Alta Matematica Francesco Severi; TUBITAK-BIDEP; University of Padovaen_US
dc.description.sponsorshipIstituto Nazionale di Alta Matematica Francesco Severi; TUBITAK-BIDEP; University of Padovaen_US
dc.identifier.doi10.1002/mma.8111
dc.identifier.endpage5387en_US
dc.identifier.issn0170-4214
dc.identifier.issn1099-1476
dc.identifier.issue9en_US
dc.identifier.scopus2-s2.0-85124596954en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.startpage5360en_US
dc.identifier.urihttps://doi.org/10.1002/mma.8111
dc.identifier.urihttps://hdl.handle.net/20.500.12415/6896
dc.identifier.volume45en_US
dc.identifier.wosWOS:000755437000001en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoenen_US
dc.publisherWileyen_US
dc.relation.ispartofMathematical Methods in The Applied Sciencesen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.snmzKY04238
dc.subjectAsymptotic Behavioren_US
dc.subjectHelmholtz Equationen_US
dc.subjectReal Analytic Continuationen_US
dc.subjectSingularly Perturbed Domainen_US
dc.subjectTransmission Problemen_US
dc.titleAsymptotic 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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