122 citations · 452 across the 56 of their papers we have counts for
62 papers
Embedding transmission problems for Maxwell's equations into elliptic theory
Yuri A. Godin, Boris Vainberg
We embed general boundary value problems for the time-harmonic Maxwell equations into the elliptic boundary value theory. This is achieved by introducing two new scalar functions t…
Spectral properties of operators and wave propagation in high-contrast media
Yuri A. Godin, Leonid Koralov, Boris Vainberg
The paper aims to study the spectral properties of elliptic operators with highly inhomogeneous coefficients and related issues concerning wave propagation in high-contrast media.…
Spectral Analysis of Lattice Schrödinger-Type Operators Associated with the Nonstationary Anderson Model and Intermittency
Dan Han, Stanislav Molchanov, Boris Vainberg
The research explores a high irregularity, commonly referred to as intermittency, of the solution to the non-stationary parabolic Anderson problem: \begin{equation*} \frac{\partial…
Local gaps in three-dimensional periodic media
Yuri A. Godin, Boris Vainberg
We consider the propagation of acoustic waves in a medium with a periodic array of small inclusions of arbitrary shape. The inclusion size is much smaller than the array period…
Propagation and dispersion of Bloch waves in periodic media with soft inclusions
Yuri A. Godin, Boris Vainberg
We investigate the behavior of waves in a periodic medium containing small soft inclusions or cavities of arbitrary shape, such that the homogeneous Dirichlet conditions are satisf…
Negative eigenvalues of non-local Schrödinger operators with sign-changing potentials
S. Molchanov, B. Vainberg
Simon's results on the negative spectrum of recurrent Schrödinger operators () are extended to a wider class of potentials and to non-local operators. An example of po…