50 Result(s)
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T. A. Shaposhnikova
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Article
Homogenization of a Parabolic Equation in a Perforated Domain with a Unilateral Dynamic Boundary Condition: Critical Case
The present paper studies the homogenization of the parabolic equation stated in a domain perforated by “tiny” balls. On the boundary of these perforations, a unilateral dynamic boundary constraints are specif...
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Article
Strange Operator in Homogenization of the Diffusion Equation in a Domain Perforated Along of a Manifold with Dynamic Signorini Condition on Perforation Boundary. Critical Case
We study the homogenization problem for the Poisson equation in a domain perforated along a manifold with the dynamic Signorini boundary condition on the boundary of perforations (particles), with a parameter ε−γ
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Article
Aperiodical Isoperimetric Planar Homogenization with Critical Diameter: Universal Non-local Strange Term for a Dynamical Unilateral Boundary Condition
We study the asymptotic behavior of the solution to the diffusion equation in a planar domain, perforated by tiny sets of different shapes with a constant perimeter and a uniformly bounded diameter, when the d...
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Article
On the Homogenization of an Optimal Control Problem in a Domain Perforated by Holes of Critical Size and Arbitrary Shape
The paper studies the asymptotic behavior of the optimal control for the Poisson type boundary value problem in a domain perforated by holes of an arbitrary shape with Robin-type boundary conditions on the int...
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Article
Appearance of a Nonlocal Monotone Operator in Transmission Conditions when Homogenizing the Poisson Equation in a Domain Perforated Along an (n − 1)-Dimensional Manifold by Sets of Arbitrary Shape and Critical Size with Nonlinear Dynamic Boundary Conditions on the Boundary of Perforations
We construct and justify an efficient model arising when homogenizing the Poisson equation in an ε-periodically perforated domain along an (n − 1)-dimensional manifold by sets of an arbitrary shape and critical s...
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Chapter and Conference Paper
Homogenization of a Parabolic Equation for p-Laplace Operator in a Domain Perforated Along \((n-1)\) -Dimensional Manifold with Dynamical Boundary Condition Specified on Perforations Boundary: Critical Case
The present paper focuses on the study of a homogenized limit of a parabolic equation for the p-Laplace operator with a nonlinear dynamical boundary condition set in a perforated domain that is obtained by removi...
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Article
Optimal Control and “Strange” Term Arising from Homogenization of the Poisson Equation in the Perforated Domain with the Robin-type Boundary Condition in the Critical Case
The present paper is devoted to the study of the asymptotic behavior of the optimal control for the boundary value problem in an ε-periodically perforated domain with linear Robin-type boundary condition, when...
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Article
A Time-Dependent Strange Term Arising in Homogenization of an Elliptic Problem with Rapidly Alternating Neumann and Dynamic Boundary Conditions Specified at the Domain Boundary: The Critical Case
A strange term arising in the homogenization of elliptic (and parabolic) equations with dynamic boundary conditions given on some boundary parts of critical size is considered. A problem with dynamic boundary ...
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Article
Homogenization of A Boundary-Value Problem in A Domain Perforated by Cavities of Arbitrary Shape with A General Nonlinear Boundary Condition On Their Boundaries: The Case of Critical Values of the Parameters
A homogenized model is constructed (with rigorous justification) for a boundary-value problem for the Poisson equation in a periodically perforated domain with a nonlinear Robin condition on the boundary of th...
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Article
Vasilii Vasilievich Zhikov
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Article
Effect of Modification of Titanium Phosphate by Hydrothermal, Microwave, and Mechanochemical Treatment on the Sorption of Cs, Sr, and U(VI) Ions
The relationship between the crystal and porous structure of titanium phosphate modified by hydrothermal, microwave, and mechanochemical treatment and its sorption characteristics with respect to Cs, Sr, and U...
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Article
Homogenization of Variational Inequalities for the p-Laplace Operator in Perforated Media Along Manifolds
We address homogenization problems of variational inequalities for the p-Laplace operator in a domain of \(\mathbb {R}^n\) ...
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Article
Homogenization Limit for the Diffusion Equation in a Domain Perforated along (n – 1)-Dimensional Manifold with Dynamic Conditions on the Boundary of the Perforations: Critical Case
The problem of homogenizing the diffusion equation in a domain perforated along an (n – 1)-dimensional manifold with dynamic boundary conditions on the boundary of the perforations is studied. A homogenized model...
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Article
Homogenization of a Boundary Value Problem for the n-Laplace Operator on a n-Dimensional Domain with Rapidly Alternating Boundary Condition Type: The Critical Case
We study the asymptotic behavior of the solution of a boundary value problem for the p-Laplace operator with rapidly alternating nonlinear boundary conditions posed on ε-periodically arranged subsets on the bound...
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Article
Homogenization of the Boundary Value Problem for the Poisson Equation with Rapidly Oscillating Nonlinear Boundary Conditions: Space Dimension n ≥ 3, Critical Case
The homogenization of the Poisson equation in a bounded domain with rapidly oscillating boundary conditions specified on a part of the domain boundary is studied. A Neumann boundary condition alternates with a...
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Article
Homogenization of Variational Inequality for the Laplace Operator with Nonlinear Constraint on the Flow in a Domain Perforated by Arbitrary Shaped Sets. Critical Case
We construct and justify a homogenized model of the variational inequality with the Laplace operator and a nonlinear boundary constraint on the flow on arbitrary shaped cavities generating perforation of the d...
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Article
Homogenization of Boundary Value Problems in Plane Domains with Frequently Alternating Type of Nonlinear Boundary Conditions: Critical Case
In the present paper we consider a boundary homogenization problem for the Poisson’s equation in a bounded domain and with a part of the boundary conditions of highly oscillating type (alternating between homo...
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Article
Non existence of critical scales in the homogenization of the problem with p-Laplace diffusion and nonlinear reaction in the boundary of periodically distributed particles in n-dimensional domains when \(p > n\)
In previous works, the homogenization of the problem with p-Laplace diffusion and nonlinear reaction in the boundary of periodically distributed particles in n-dimensional domains has been studied in the cases wh...
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Article
Homogenization of the boundary value problem for the Laplace operator in a domain perforated along (n – 1)-dimensional manifold with nonlinear Robin type boundary condition on the boundary of arbitrary shaped holes: Critical case
The asymptotic behavior of the solution to the boundary value problem for the Laplace operator in a domain perforated along an (n − 1)-dimensional manifold is studied. A nonlinear Robin-type condition is assumed ...
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Article
Homogenization of the boundary value problem for the laplace operator in a perforated domain with a rapidly oscillating nonhomogeneous Robin-type condition on the boundary of holes in the critical case
The asymptotic behavior of solutions to a boundary value problem in a domain periodically perforated by small holes with a rapidly oscillating nonhomogeneous Robin-type condition on their boundaries is investi...
