11 citations · 19 across the 9 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…
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…
On band gaps in photonic crystal fibers
Shane Cooper, Ilia Kamotski, Valery Smyshlyaev
We consider the Maxwell's system for a periodic array of dielectric `fibers' embedded into a `matrix', with respective electric permittivities and , which serves as a mo…
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…
Refined Scattering and Hermitian Spectral Theory for Linear Higher-Order Schrödinger Equations
V. A. Galaktionov, I. V. Kamotski
A classification of large-time and finite-time blow-up asymptotics of solutions of the Cauchy problem for higher-order Schrödinger equations is performed.