33 citations · 184 across the 24 of their papers we have counts for
26 papers
Sobolev multipliers and fractional Gaussian fields on Lipschitz boundaries with applications to deterministic and random acoustic systems
Illya M. Karabash
Motivated by Applied Physics and Photonics studies of random resonators, we study in the stochastic part of this paper random acoustic operators in non-smooth bounded domains $G \s…
M-dissipative generalized impedance boundary conditions, discrete spectra, and pointwise multipliers between fractional Sobolev spaces
Illya M. Karabash
The paper studies properties of acoustic operators in bounded Lipschitz domains with m-dissipative generalized impedance boundary conditions. We prove that such acoustic operat…
Random acoustic boundary conditions and Weyl's law for Laplace-Beltrami operators on non-smooth boundaries
Illya M. Karabash
Motivated by engineering and photonics research on resonators in random or uncertain environments, we study rigorous randomizations of boundary conditions for wave equations of the…
Multi-parameter Hopf bifurcations of rimming flows
Illya M. Karabash, Christina Lienstromberg, Juan J. L. Velázquez
In order to investigate the emergence of periodic oscillations of rimming flows, we study analytically the stability of steady states for the model of (Benilov, Kopteva, O'Brien, 2…
Homogenization and nonselfadjoint spectral optimization for dissipative Maxwell eigenproblems
Matthias Eller, Illya M. Karabash
The homogenization of eigenvalues of non-Hermitian Maxwell operators is studied by the H-convergence method. It is assumed that the Maxwell systems are equipped with suitable m-dis…
M-dissipative boundary conditions and boundary tuples for Maxwell operators
Matthias Eller, Illya M. Karabash
For Maxwell operators in Lipschitz domains, we describe all m-dissipative boundary conditions and apply this result…
Asymptotics of random resonances generated by a point process of delta-interactions
Sergio Albeverio, Illya M. Karabash
We introduce and study the following model for random resonances: we take a collection of point interactions generated by a simple finite point process in the 3-D space and c…
Euler-Lagrange equations for full topology optimization of the Q-factor in leaky cavities
Matthias Eller, Illya M. Karabash
We derive Euler-Lagrange equations for the topology optimization of decay rate in 3-d lossy optical cavities. This leads to a new class of time-harmonic differential or integro-dif…
Pareto optimization of resonances and minimum-time control
Illya M. Karabash, Herbert Koch, Ievgen V. Verbytskyi
The aim of the paper is to reduce one spectral optimization problem, which involves the minimization of the decay rate of a resonance , to a collection of…
On the multilevel internal structure of the asymptotic distribution of resonances
Sergio Albeverio, Illya M. Karabash
We prove that the asymptotic distribution of resonances has a multilevel internal structure for the following classes of Hamiltonians H: Schrödinger operators with point interactio…
Generic asymptotics of resonance counting function for Schrödinger point interactions
Sergio Albeverio, Illya M. Karabash
We study the leading coefficient in the asymptotical formula , , for the resonance counting function of Schrödinger Hamilton…
Resonance free regions and non-Hermitian spectral optimization for Schrödinger point interactions
Sergio Albeverio, Illya M. Karabash
Resonances of Schrödinger Hamiltonians with point interactions are considered. The main object under the study is the resonance free region under the assumption that the centers, w…
Recovery of periodicities hidden in heavy-tailed noise
Illya M. Karabash, Jürgen Prestin
We address a parametric joint detection-estimation problem for discrete signals of the form , , with an additive no…
Nonlinear bang-bang eigenproblems and optimization of resonances in layered cavities
Illya M. Karabash, Olga M. Logachova, Ievgen V. Verbytskyi
Quasi-normal-eigenvalue optimization is studied under constraints on structure functions of 2-side open optical or mechanical resonators. We prove…
Pareto optimal structures producing resonances of minimal decay under -type constraints
Illya M. Karabash
Optimization of resonances associated with 1-D wave equations in inhomogeneous media is studied under the constraint on the nonnegative function $B \in L^1 (0,\ell…
Structured stability radii and exponential stability tests for Volterra difference systems
Elena Braverman, Illya Karabash
Uniform exponential (UE) stability of linear difference equations with infinite delay is studied using the notions of a stability radius and a phase space. The state space $\X$ is…
Nonlinear eigenvalue problem for optimal resonances in optical cavities
I. M. Karabash
The paper is devoted to optimization of resonances in a 1-D open optical cavity. The cavity's structure is represented by its dielectric permittivity function e(s). It is assumed t…
Optimization of quasi-normal eigenvalues for Krein-Nudelman strings
Illya M. Karabash
The paper is devoted to optimization of resonances for Krein strings with total mass and statical moment constraints. The problem is to design for a given a string that h…
Optimization of quasi-normal eigenvalues for 1-D wave equations in inhomogeneous media; description of optimal structures
Illya M. Karabash
The paper is devoted to optimization of resonances associated with 1-D wave equations in inhomogeneous media. The medium's structure is represented by a nonnegative function B. The…
Bohl-Perron type stability theorems for linear difference equations with infinite delay
Elena Braverman, Illya M. Karabash
Relation between two properties of linear difference equations with infinite delay is investigated: (i) exponential stability, (ii) -input -state stability (sometimes is…
A functional model, eigenvalues, and finite singular critical points for indefinite Sturm-Liouville operators
I. M. Karabash
Eigenvalues in the essential spectrum of a weighted Sturm-Liouville operator are studied under the assumption that the weight function has one turning point. An abstract approach t…
On the nature of ill-posedness of the forward-backward heat equation
Marina Chugunova, Illya M. Karabash, Sergei G. Pyatkov
We study the Cauchy problem with periodic initial data for the forward-backward heat equation defined by the J-self-adjoint linear operator L depending on a small parameter. The pr…
Abstract kinetic equations with positive collision operators
I. M. Karabash
We consider "forward-backward" parabolic equations in the abstract form , , where and are operators in a Hilbert space such th…
Spectral properties of singular Sturm-Liouville operators with indefinite weight sgn x
I. Karabash, C. Trunk
We consider a singular Sturm-Liouville expression with the indefinite weight sgn x. To this expression there is naturally a self-adjoint operator in some Krein space associated. We…