Authors: | Schweizer, Ben |
Title: | Existence results for the Helmholtz equation in periodic wave-guides with energy methods |
Language (ISO): | en |
Abstract: | The Helmholtz equation $ - \nabla \cdot (a \nabla u) - \omega^2 u = f$ is considered in an unbounded wave-guide $\Omega := \mathbb{R} \times S \subset \mathbb{R}^d$, where $S \subset \mathbb{R}^{d-1}$ is a bounded domain. The coefficient $a$ is strictly elliptic and (locally) periodic in the unbounded direction $x_1\in \mathbb{R}$. For non-singular frequencies $\omega$, we show the existence of a solution $u$. While previous proofs of such results were based on operator theory, our proof uses only energy methods. |
Subject Headings: | Helmholtz equation wave-guide periodic media Fredholm alternative |
URI: | http://hdl.handle.net/2003/38161 http://dx.doi.org/10.17877/DE290R-20140 |
Issue Date: | 2019-05-10 |
Appears in Collections: | Preprints der Fakultät für Mathematik Schweizer, Ben Prof. Dr. |
Files in This Item:
File | Description | Size | Format | |
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Preprint 2019-03.pdf | DNB | 466.67 kB | Adobe PDF | View/Open |
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