30 citations · 94 across the 17 of their papers we have counts for
20 papers
Norm-resolvent asymptotics for the Neumann Laplacian on periodic resonant thin structures
Kirill Cherednichenko, Chuanjie Wu
We consider the Neumann Laplacian on a three-dimensional periodic network of thin rods with edge thickness of order and vertex diameter of order . We extend the fixed-…
Homogenized graphs with spectrally embedded defect states
Kirill D. Cherednichenko, Stephen P. Shipman
By homogenizing high-contrast periodic metric graphs, we create continuous media that admit bound states produced by local defects at energies embedded in the continuous spectrum.…
Effective behaviour of critical-contrast PDEs: micro-resonances, frequency conversion, and time dispersive properties. II
Kirill Cherednichenko, Alexander Kiselev, Igor Velčić +1
We construct an order-sharp theory for a double-porosity model in the full linear elasticity setup. Crucially, we uncover time and frequency dispersive properties of highly oscilla…
Norm-resolvent convergence for Neumann Laplacians on manifolds thinning to graphs
Kirill D. Cherednichenko, Yulia Yu. Ershova, Alexander V. Kiselev
Norm-resolvent convergence with order-sharp error estimate is established for Neumann Laplacians on thin domains in converging to metric graphs in the limi…
Asymptotic analysis of operator families and applications to resonant media
Kirill D. Cherednichenko, Yulia Yu. Ershova, Alexander V. Kiselev +2
We give an overview of operator-theoretic tools that have recently proved useful in the analysis of boundary-value and transmission problems for second-order partial differential e…
Operator-norm resolvent estimates for thin elastic periodically heterogeneous rods in moderate contrast
Kirill Cherednichenko, Igor Velčić, Josip Žubrinić
We provide resolvent asymptotics as well as various operator-norm estimates for the system of linear partial differential equations describing the thin infinite elastic rod with ma…
Functional model for generalised resolvents and its application to time-dispersive media
Kirill D. Cherednichenko, Yulia Yu. Ershova, Sergey N. Naboko
Motivated by recent results concerning the asymptotic behaviour of differential operators with highly contrasting coefficients, which have involved effective descriptions involving…
Spatial non-locality of the Maxwell system on periodic structures
Kirill Cherednichenko, Serena D'Onofrio
For we analyse the Maxwell system of equations of electromagnetism on -periodic sets Assuming that a family of Bo…
Functional model for boundary-value problems
Kirill D. Cherednichenko, Alexander V. Kiselev, Luis O. Silva
We develop a functional model for operators arising in the study of boundary-value problems of materials science and mathematical physics. We then provide explicit formulae for the…
Operator-norm homogenisation estimates for the system of Maxwell equations on periodic singular structures
Kirill Cherednichenko, Serena D'Onofrio
For arbitrarily small values of we formulate and analyse the Maxwell system of equations of electromagnetism on -periodic sets $S^\varepsilon\subset{\…
Effective behaviour of critical-contrast PDEs: micro-resonances, frequency conversion, and time dispersive properties. I
Kirill Cherednichenko, Yulia Ershova, Alexander Kiselev
A novel approach to critical-contrast homogenisation for periodic PDEs is proposed, via an explicit asymptotic analysis of Dirichlet-to-Neumann operators. Norm-resolvent asymptotic…
Unified approach to critical-contrast homogenisation with explicit links to time-dispersive media
Kirill Cherednichenko, Yulia Ershova, Alexander Kiselev +1
A novel approach to critical-contrast homogenisation is proposed. Norm-resolvent asymptotics are explicitly constructed. An essential feature of our approach is that it relates hom…
Time-Dispersive Behaviour as a Feature of Critical Contrast Media
Kirill Cherednichenko, Yulia Ershova, Alexander V. Kiselev
Motivated by the urgent need to attribute a rigorous mathematical meaning to the term "metamaterial", we propose a novel approach to the homogenisation of critical-contrast composi…
Sharp operator-norm asymptotics for thin elastic plates with rapidly oscillating periodic properties
Kirill Cherednichenko, Igor Velčić
We analyse a system of partial differential equations describing the behaviour of an elastic plate with periodic moduli in the two planar directions, in the asymptotic regime when…
Operator-norm convergence estimates for elliptic homogenisation problems on periodic singular structures
Kirill Cherednichenko, Serena D'Onofrio
For a an arbitrary periodic Borel measure , we prove order operator-norm resolvent estimates for the solutions to scalar elliptic problems in $L^2({\mathbb R}^d…
Scattering theory for a class of non-selfadjoint extensions of symmetric operators
Kirill D. Cherednichenko, Alexander V. Kiselev, Luis O. Silva
This work deals with the functional model for a class of extensions of symmetric operators and its applications to the theory of wave scattering. In terms of Boris Pavlov's spectra…
Resolvent estimates in homogenisation of periodic problems of fractional elasticity
Kirill Cherednichenko, Marcus Waurick
We provide operator-norm convergence estimates for solutions to a time-dependent equation of fractional elasticity in one spatial dimension, with rapidly oscillating coefficients t…
Functional model for extensions of symmetric operators and applications to scattering theory
Kirill D. Cherednichenko, Alexander V. Kiselev, Luis O. Silva
On the basis of the explicit formulae for the action of the unitary group of exponentials corresponding to almost solvable extensions of a given closed symmetric operator with equa…
Homogenisation of thin periodic frameworks with high-contrast inclusions
Kirill D. Cherednichenko, James A. Evans
We analyse a problem of two-dimensional linearised elasticity for a two-component periodic composite, where one of the components consists of disjoint soft inclusions embedded in a…
Norm-resolvent convergence of one-dimensional high-contrast periodic problems to a Kronig-Penney dipole-type model
Kirill D. Cherednichenko, Alexander V. Kiselev
We prove operator-norm resolvent convergence estimates for one-dimensional periodic differential operators with rapidly oscillating coefficients in the non-uniformly elliptic high-…