Homogenization and uniform stabilization for a nonlinear hyperbolic equation in domains with holes of small capacity.
Homogenization of a quasi-linear problem with quadratic growth in perforated domains : an example
Homogenization of almost periodic monotone operators
Homogenization of elliptic problems in a fiber reinforced structure. Non local effects
Homogenization of linear elasticity equations
The homogenization problem (i.e. the approximation of the material with periodic structure by a homogeneous one) for linear elasticity equation is studied. Both formulations in terms of displacements and in terms of stresses are considered and the results compared. The homogenized equations are derived by the multiple-scale method. Various formulae, properties of the homogenized coefficients and correctors are introduced. The convergence of displacment vector, stress tensor and local energy is proved...
Homogenization of nonlinear monotone operators beyond the periodic setting.
Homogenization of -laplacian in perforated domain
Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1
We consider quasilinear optimal control problems involving a thick two-level junction Ωε which consists of the junction body Ω0 and a large number of thin cylinders with the cross-section of order 𝒪(ε2). The thin cylinders are divided into two levels depending on the geometrical characteristics, the quasilinear boundary conditions and controls given on their lateral surfaces and bases respectively. In addition, the quasilinear boundary conditions depend on parameters ε, α, β and the...
Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1∗
We consider quasilinear optimal control problems involving a thick two-level junction Ωε which consists of the junction body Ω0 and a large number of thin cylinders with the cross-section of order 𝒪(ε2). The thin cylinders are divided into two levels depending on the geometrical characteristics, the quasilinear boundary conditions and controls given on their lateral surfaces and bases respectively. In addition, the quasilinear boundary...
Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1∗
We consider quasilinear optimal control problems involving a thick two-level junction Ωε which consists of the junction body Ω0 and a large number of thin cylinders with the cross-section of order 𝒪(ε2). The thin cylinders are divided into two levels depending on the geometrical characteristics, the quasilinear boundary conditions and controls given on their lateral surfaces and bases respectively. In addition, the quasilinear boundary...
Homogenization of the Poisson equation in a thick periodic junction.
Homogenization with uncertain input parameters
We homogenize a class of nonlinear differential equations set in highly heterogeneous media. Contrary to the usual approach, the coefficients in the equation characterizing the material properties are supposed to be uncertain functions from a given set of admissible data. The problem with uncertainties is treated by means of the worst scenario method, when we look for a solution which is critical in some sense.
Hyperbolic boundary value problem with equivalued surface on a domain with thin layer
This paper deals with a kind of hyperbolic boundary value problems with equivalued surface on a domain with thin layer. Existence and uniqueness of solutions are given, and the limit behavior of solutions is studied in this paper.
Hyperbolic Equations in Uniform Spaces
The paper is devoted to the Cauchy problem for a semilinear damped wave equation in the whole of ℝ ⁿ. Under suitable assumptions a bounded dissipative semigroup of global solutions is constructed in a locally uniform space . Asymptotic compactness of this semigroup and the existence of a global attractor are then shown.
Hyperbolic Perturbation Problems Involving Time Derivatives on the Boundars.