5 papers · 1 filter
Eigenvalues of the truncated Helmholtz solution operator under strong trapping
Jeffrey Galkowski, Pierre Marchand, Euan A. Spence
For the Helmholtz equation posed in the exterior of a Dirichlet obstacle, we prove that if there exists a family of quasimodes (as is the case when the exterior of the obstacle has…
For most frequencies, strong trapping has a weak effect in frequency-domain scattering
David Lafontaine, Euan A. Spence, Jared Wunsch
It is well known that when the geometry and/or coefficients allow stable trapped rays, the outgoing solution operator of the Helmholtz equation (a.k.a. the resolvent of the Laplaci…
Optimal constants in nontrapping resolvent estimates and applications in numerical analysis
Jeffrey Galkowski, Euan A. Spence, Jared Wunsch
We study the resolvent for nontrapping obstacles on manifolds with Euclidean ends. It is well known that for such manifolds, the outgoing resolvent satisfies $\|χR(k) χ\|_{L^2\to L…
Wavenumber-explicit regularity estimates on the acoustic single- and double-layer operators
Jeffrey Galkowski, Euan A. Spence
We prove new, sharp, wavenumber-explicit bounds on the norms of the Helmholtz single- and double-layer boundary-integral operators as mappings from $L^2(\partial Ω)\rightarrow H^1(…
The Helmholtz equation in random media: well-posedness and a priori bounds
O. R. Pembery, E. A. Spence
We prove well-posedness results and a priori bounds on the solution of the Helmholtz equation , posed either in or in the exte…