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1.	Chechkin, G.A., et al. (author) On the Friedrichs inequality in a domain perforated aperiodically along the boundary : Homogenization procedure. Asymptotics for parabolic problems 2009 In: Russian journal of mathematical physics. - 1061-9208 .- 1555-6638. ; 16:1, s. 1-16 Journal article (peer-reviewed)abstract This paper is devoted to the asymptotic analysis of functions depending on a small parameter characterizing the microinhomogeneous structure of the domain on which the functions are defined. We derive the Friedrichs inequality for these functions and prove the convergence of solutions to corresponding problems posed in a domain perforated aperiodically along the boundary. Moreover, we use numerical simulation to illustrate the results.
2.	Chechkin, G. A., et al. (author) On the precise asymptotics of the constant in Friedrich's inequality for functions vanishing on the part of the boundary with microinhomogeneous structure 2007 In: Journal of inequalities and applications. - : Springer Science and Business Media LLC. - 1025-5834 .- 1029-242X. Journal article (peer-reviewed)abstract We construct the asymptotics of the sharp constant in the Friedrich-type inequality for functions, which vanish on the small part of the boundary Γ1ɛ. It is assumed that Γ1ɛ consists of (1/δ)n-1 pieces with diameter of order O(ɛδ). In addition, δ=δ(ɛ) and δ→0 as ɛ→0.
3.	Gadyl'shin, R. R., et al. (author) On the asymptotic behavior of a simple eigenvalue of a boundary value problem in a domain perforated along the boundary 2011 In: Differential equations. - 0012-2661 .- 1608-3083. ; 47:6, s. 822-831 Journal article (peer-reviewed)abstract We consider a boundary value problem for the Laplace operator in a model domain periodically perforated along the boundary. We assume that the homogeneous Neumann condition is posed on the exterior boundary and the homogeneous Dirichlet condition is posed on the boundary of the cavities. We construct and justify the asymptotic expansions of eigenelements of the boundary value problem.

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Type of publication: journal article (3)

Type of content: peer-reviewed (3)

Author/Editor: Koroleva, Yulia O. (3); Persson, Lars-Erik (2); Chechkin, G.A. (2); Chechkin, Gregory A. (1); Meidell, Annette (1); Gadyl'shin, R. R. (1)

University: Luleå University of Technology (3); Uppsala University (1)

Language: English (3)

Research subject (UKÄ/SCB): Natural sciences (3)

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