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Generalization of unfolding operator for highly oscillating smooth boundary domains and homogenization
Unfolding operators have been introduced and used to study homogenization problems.
Initially, they were introduced for problems with rapidly oscillating coefficients and porous …
Initially, they were introduced for problems with rapidly oscillating coefficients and porous …
[HTML][HTML] Homogenization of a nonlinear monotone problem with nonlinear Signorini boundary conditions in a domain with highly rough boundary
In this paper, we consider a domain Ω ε⊂ RN, N≥ 2, with a very rough boundary depending
on ε. For instance, if N= 3 Ω ε has the form of a brush with an ε-periodic distribution of thin …
on ε. For instance, if N= 3 Ω ε has the form of a brush with an ε-periodic distribution of thin …
Junction problem for thin elastic and volume rigid inclusions in elastic body
The article concerns a junction problem for two-dimensional elastic body with a thin elastic
inclusion and a volume rigid inclusion. It is assumed that the inclusions have a common …
inclusion and a volume rigid inclusion. It is assumed that the inclusions have a common …
Semi-linear optimal control problem on a smooth oscillating domain
We demonstrate the asymptotic analysis of a semi-linear optimal control problem posed on a
smooth oscillating boundary domain in the present paper. We have considered a more …
smooth oscillating boundary domain in the present paper. We have considered a more …
Optimal control problem in a domain with branched structure and homogenization
We consider a linear parabolic problem in a thick junction domain which is the union of a
fixed domain and a collection of periodic branched trees of height of order 1 and small width …
fixed domain and a collection of periodic branched trees of height of order 1 and small width …
Optimal control of rigidity parameters of thin inclusions in composite materials
In the paper, an equilibrium problem for an elastic body with a thin elastic and a volume rigid
inclusion is analyzed. It is assumed that the thin inclusion conjugates with the rigid inclusion …
inclusion is analyzed. It is assumed that the thin inclusion conjugates with the rigid inclusion …
A two-dimensional electrostatic model of interdigitated comb drive in longitudinal mode
A periodic homogenization model of the electrostatic equation is constructed for a comb
drive with a large number of fingers and whose mode of operation is in-plane and …
drive with a large number of fingers and whose mode of operation is in-plane and …
[HTML][HTML] Asymptotic approximation for the solution to a semi-linear parabolic problem in a thick junction with the branched structure
We consider a semi-linear parabolic problem in a thick junction Ω ε, which is the union of a
domain Ω 0 and a lot of joined thin trees situated ε-periodically along some manifold on the …
domain Ω 0 and a lot of joined thin trees situated ε-periodically along some manifold on the …
On critical parameters in homogenization of perforated domains by thin tubes with nonlinear flux and related spectral problems
Let uϵ be the solution of the Poisson equation in a domain perforated by thin tubes with a
nonlinear Robin‐type boundary condition on the boundary of the tubes (the flux here being …
nonlinear Robin‐type boundary condition on the boundary of the tubes (the flux here being …
[HTML][HTML] Exact controllability for evolutionary imperfect transmission problems
In this paper we study the asymptotic behaviour of an exact controllability problem for a
second order linear evolution equation defined in a two-component composite with ε …
second order linear evolution equation defined in a two-component composite with ε …