Operator estimates for non-periodically perforated domains with Dirichlet and nonlinear Robin conditions: vanishing limit

DI Borisov, J Kříž - Analysis and Mathematical Physics, 2023 - Springer
We consider a general second order linear elliptic equation in a finely perforated domain.
The shapes of cavities and their distribution in the domain are arbitrary and non-periodic; …

Operator estimates for homogenization of the Robin Laplacian in a perforated domain

A Khrabustovskyi, M Plum - Journal of Differential Equations, 2022 - Elsevier
Let ε> 0 be a small parameter. We consider the domain Ω ε:= Ω∖ D ε, where Ω is an open
domain in R n, and D ε is a family of small balls of the radius d ε= o (ε) distributed …

Operator estimates for non‐periodically perforated domains with Dirichlet and nonlinear Robin conditions: Strange term

DI Borisov - Mathematical Methods in the Applied Sciences, 2024 - Wiley Online Library
We consider a boundary value problem for a general second‐order linear equation in a
domain with a fine perforation. The latter is made by small cavities; both the shapes of the …

Operator estimates for non-periodically perforated domains: disappearance of cavities

DI Borisov - Applicable Analysis, 2024 - Taylor & Francis
We consider a boundary value problem for a general second-order linear equation in a
perforated domain. The perforation is made by small cavities, a minimal distance between …

On the convergence of controls and cost functionals in some optimal control heterogeneous problems when the homogenization process gives rise to some strange …

JI Díaz, AV Podolskiy, TA Shaposhnikova - Journal of Mathematical …, 2022 - Elsevier
We consider the convergence of solutions and cost functional in some optimal control
problems arising in the study of the adsorption chemical phenomenon in which some …

Unexpected regionally negative solutions of the homogenization of Poisson equation with dynamic unilateral boundary conditions: critical symmetric particles

JI Díaz, AV Podolskiy, TA Shaposhnikova - Revista de la Real Academia …, 2024 - Springer
We obtain the homogenized problem associated with the Poisson equation in a domain
perforated by" tiny" balls (or in a domain defined as the exterior to a periodic set of very small …

[HTML][HTML] On the corrector term in the homogenization of the nonlinear Poisson-Robin problem giving rise to a strange term: Application to an optimal control problem

JI Díaz, AV Podolskiy, TA Shaposhnikova - Journal of Mathematical …, 2025 - Elsevier
We consider the homogenization process corresponding to some heterogeneous problems
that are given by the Poisson equation with a nonlinear Robin-type boundary conditions on …

Aperiodical isoperimetric planar homogenization with critical diameter: universal non-local strange term for a dynamical unilateral boundary condition

JI Díaz, TA Shaposhnikova, AV Podolskiy - Doklady Mathematics, 2024 - Springer
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 …

On p-Laplacian Reaction–Diffusion Problems with Dynamical Boundary Conditions in Perforated Media

M Anguiano - Mediterranean Journal of Mathematics, 2023 - Springer
We study the effect of the p-Laplacian operator in the modelling of the heat equation through
a porous medium Λ ϵ⊂ RN (N≥ 2). The case of p= 2 was recently published in Anguiano …

Norm convergence for problems with perforation along a given manifold with nonlinear Robin condition on boundaries of cavities

DI Borisov, AI Mukhametrakhimova - arxiv preprint arxiv:2202.10767, 2022 - arxiv.org
In the work we consider a boundary value problem for a second order equation with variable
coefficients in a multi-dimensional domain perforated by small cavities closely spaced along …