Authors: | Schweizer, Ben |
Title: | Inhomogeneous Helmholtz equations in wave guides – existence and uniqueness results with energy methods |
Language (ISO): | en |
Abstract: | The 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. |
Subject Headings: | Helmholtz equation Wave guide Periodic media Fredholm alternative |
URI: | http://hdl.handle.net/2003/41322 http://dx.doi.org/10.17877/DE290R-23165 |
Issue Date: | 2022-03-30 |
Rights link: | https://creativecommons.org/licenses/by/4.0/ |
Appears in Collections: | Lehrstuhl I Analysis |
Files in This Item:
File | Description | Size | Format | |
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inhomogeneous-helmholtz-equations-in-wave-guides-existence-and-uniqueness-results-with-energy-methods.pdf | 452.06 kB | Adobe PDF | View/Open |
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