6. Februar 2020
Vortragender: Prof. Dr. Ben Schweizer (TU Dortmund)
Vortragstitel: Difficulties in the analysis of the Helmholtz equation
Abstrakt:
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.