Existence results for the Helmholtz equation in periodic wave-guides with energy methods
| dc.contributor.author | Schweizer, Ben | |
| dc.date.accessioned | 2019-08-02T13:32:10Z | |
| dc.date.available | 2019-08-02T13:32:10Z | |
| dc.date.issued | 2019-05-10 | |
| dc.description.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. | en |
| dc.identifier.uri | http://hdl.handle.net/2003/38161 | |
| dc.identifier.uri | http://dx.doi.org/10.17877/DE290R-20140 | |
| dc.language.iso | en | |
| dc.relation.ispartofseries | Preprint;2019-3 | |
| dc.subject | Helmholtz equation | en |
| dc.subject | wave-guide | en |
| dc.subject | periodic media | en |
| dc.subject | Fredholm alternative | en |
| dc.subject.ddc | 610 | |
| dc.title | Existence results for the Helmholtz equation in periodic wave-guides with energy methods | de |
| dc.type | Text | de |
| dc.type.publicationtype | preprint | en |
| dcterms.accessRights | open access | |
| eldorado.secondarypublication | false |