34 citations · 52 across the 7 of their papers we have counts for
9 papers
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…
Bandgaps in two-dimensional high-contrast periodic elastic beam lattice materials
I. V. Kamotski, V. P. Smyshlyaev
We consider elastic waves in a two-dimensional periodic lattice network of Timoshenko-type beams. We show that for general configurations involving certain highly-contrasting compo…
Contour integral solutions of the parabolic wave equation
David P. Hewett, John R. Ockendon, Valery P. Smyshlyaev
We present a simple systematic construction and analysis of solutions of the two-dimensional parabolic wave equation that exhibit far-field localisation near a given algebraic plan…
Localised modes due to defects in high contrast periodic media via two-scale homogenization
I. V. Kamotski, V. P. Smyshlyaev
The spectral problem for an infinite periodic medium perturbed by a compact defect is considered. For a high contrast small $\ve$-size periodicity and a finite size defect we consi…
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…