Inhomogeneous Helmholtz equations in wave guides – existence and uniqueness results with energy methods

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dc.contributor.authorSchweizer, Ben
dc.date.accessioned2023-04-06T07:07:14Z
dc.date.available2023-04-06T07:07:14Z
dc.date.issued2022-03-30
dc.description.abstractThe Helmholtz equation −∇⋅(a∇u)−ω2u=f is considered in an unbounded wave guide Ω:=R×S⊂Rd , S⊂Rd−1 a bounded domain. The coefficient a is strictly elliptic and either periodic in the unbounded direction x1∈R or periodic outside a compact subset; in the latter case, two different periodic media can be used in the two unbounded directions. For non-singular frequencies ω , we show the existence of a solution u. While previous proofs of such results were based on analyticity arguments within operator theory, here, only energy methods are used.en
dc.identifier.urihttp://hdl.handle.net/2003/41322
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-23165
dc.language.isoende
dc.relation.ispartofseriesEuropean journal of applied mathematics;34(2)
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectHelmholtz equationen
dc.subjectWave guideen
dc.subjectPeriodic mediaen
dc.subjectFredholm alternativeen
dc.subject.ddc510
dc.titleInhomogeneous Helmholtz equations in wave guides – existence and uniqueness results with energy methodsen
dc.typeTextde
dc.type.publicationtypearticlede
dcterms.accessRightsopen access
eldorado.secondarypublicationtruede
eldorado.secondarypublication.primarycitationSCHWEIZER, B. (2023). Inhomogeneous Helmholtz equations in wave guides – existence and uniqueness results with energy methods. European Journal of Applied Mathematics, 34(2), 211-237. doi:10.1017/S0956792522000080de
eldorado.secondarypublication.primaryidentifierhttps://doi.org/10.1017/S0956792522000080de

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