30 citations · 55 across the 10 of their papers we have counts for
10 papers
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…
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…
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…
Isospectrality for graph Laplacians under the change of coupling at graph vertices: necessary and sufficient conditions
Yulia Ershova, Irina I. Karpenko, Alexander V. Kiselev
Laplace operators on finite compact metric graphs are considered under the assumption that matching conditions at graph vertices are of and types. Assuming rational indepe…
Isospectrality for graph Laplacians under the change of coupling at graph vertices
Yulia Ershova, Irina I. Karpenko, Alexander V. Kiselev
Laplacian operators on finite compact metric graphs are considered under the assumption that matching conditions at graph vertices are of and types. An infinite series of…
Trace formulae for Schrodinger operators on metric graphs with applications to recovering matching conditions
Yulia Ershova, Alexander V. Kiselev
The paper is a continuation of the study started in \cite{Yorzh1}. Schrodinger operators on finite compact metric graphs are considered under the assumption that the matching condi…
Trace formulae for graph Laplacians with applications to recovering matching conditions
Yulia Ershova, Alexander V. Kiselev
Graph Laplacians on finite compact metric graphs are considered under the assumption that the matching conditions at the graph vertices are of either or type. In either ca…