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Ben Schweizer: "Difficulties in the analysis of the Helmholtz equation"
| Termin |
Donnerstag, 6. Februar 2020, 16.15 - 18.00 Uhr
|
| Veranstaltungsart |
Kolloquium |
| Reihe |
Kolloquium des Instituts für Mathematik
|
| Einrichtung |
Naturwissenschaftliche Fakultät II |
| Veranstalter |
Institut für Mathematik |
| Veranstaltungsort |
Informatikgebäude, Hörsaal 1.04 |
| Straße |
Von-Seckendorff-Platz 1 |
| PLZ/Ort |
06120 Halle |
Beschreibung
The Helmholtz equation describes wave phenomena. It looks innocent:
For a given positive coefficient field "a" and a given frequency "\omega>0", the unknown "u" shall solve the linear elliptic equation "-\nabla\cdot (a \nabla u) = \omega^2 u". The important feature of the equation is the sign of the different terms; the equation possesses nontrivial (wave-like) solutions even for homogeneous boundary conditions. We discuss three phenomena: 1) The behavior of solutions in a domain with small inclusions. 2) Boundary conditions at infinity and truncations of unbounded domains. 3) Existence results in unbounded domains.
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