34 citations · 52 across the 7 of their papers we have counts for
4 papers · 1 filter
Quantitative multiscale operator-type approximations for asymptotically degenerating spectral problems
Shane Cooper, Ilia Kamotski, Valery P. Smyshlyaev
We study an abstract family of asymptotically degenerating variational problems. Those are natural generalisations of families of problems emerging upon application of a rescaled F…
Searchlight Asymptotics for High-Frequency Scattering by Boundary Inflection
V. P. Smyshlyaev, I. V. Kamotski
We consider an inner problem for whispering gallery high-frequency asymptotic mode's scattering by a boundary inflection. The related boundary-value problem for a Schrödinger equat…
High-frequency bounds for the Helmholtz equation under parabolic trapping and applications in numerical analysis
Simon N. Chandler-Wilde, Euan A. Spence, Andrew Gibbs +1
This paper is concerned with resolvent estimates on the real axis for the Helmholtz equation posed in the exterior of a bounded obstacle with Dirichlet boundary conditions when the…
Two-scale homogenization for a general class of high contrast PDE systems with periodic coefficients
I. V. Kamotski, V. P. Smyshlyaev
For two-scale homogenization of a general class of asymptotically degenerating %uniformly strongly elliptic symmetric PDE systems with a critically scaled high contrast in periodic…