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
periodic media
Fredholm alternative
Issue Date: 2019-05-10
Appears in Collections:Preprints der Fakultät für Mathematik
Schweizer, Ben Prof. Dr.

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