Abstract:
For the case of a 2-connected ε-periodic (ε∈(0,1)) perforated space with a bounded domain Ωε selected in it the homogenization property as
ε→0 is proved for the boundary-value problem for a second-order elliptic operator in the domain Ωε with one-sided condition of Signorini type on the boundaries of “cavities” and with Dirichlet condition on the outer boundary.
Citation:
S. E. Pastukhova, “Homogenization of a mixed problem with Signorini condition for an elliptic operator in a perforated domain”, Sb. Math., 192:2 (2001), 245–260
\Bibitem{Pas01}
\by S.~E.~Pastukhova
\paper Homogenization of a~mixed problem with Signorini condition for an~elliptic operator in a~perforated domain
\jour Sb. Math.
\yr 2001
\vol 192
\issue 2
\pages 245--260
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\crossref{https://doi.org/10.1070/sm2001v192n02ABEH000544}
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Linking options:
https://www.mathnet.ru/eng/sm544
https://doi.org/10.1070/sm2001v192n02ABEH000544
https://www.mathnet.ru/eng/sm/v192/i2/p87
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J. I. Díaz, T. A. Shaposhnikova, A. V. Podolskiy, “Aperiodical Isoperimetric Planar Homogenization with Critical Diameter: Universal Non-local Strange Term for a Dynamical Unilateral Boundary Condition”, Dokl. Math., 2024
A. V. Podolskiy, T. A. Shaposhnikova, “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”, J Math Sci, 279:4 (2024), 525
J. I. Diaz, T. A. Shaposhnikova, A. V. Podolskiy, “Aperiodical isoperimetric planar homogenization with critical diameter: universal non-local strange term for a dynamical unilateral boundary condition”, Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, 515:1 (2024), 18
Jake Avila, “Homogenization and corrector results of elliptic problems with Signorini boundary conditions in perforated domains”, Annali di Matematica, 2024
Ptashnyk M., “Homogenization of Some Degenerate Pseudoparabolic Variational Inequalities”, J. Math. Anal. Appl., 469:1 (2019), 44–75
Gomez D., Lobo M., Perez E., Podolskii V A., Shaposhnikova T.A., “Unilateral Problems For the P-Laplace Operator in Perforated Media Involving Large Parameters”, ESAIM-Control OPtim. Calc. Var., 24:3 (2018), 921–964
Amirat Y., Shelukhin V.V., “Homogenization of composite electrets”, Eur. J. Appl. Math., 28:2 (2017), 261–283
T. A. Mel’nyk, Iu. A. Nakvasiuk, “Homogenization of a parabolic signorini boundary value problem in a thick plane junction”, J Math Sci, 2012
T. A. Mel'nyk, Iu. A. Nakvasiuk, W. L. Wendland, “Homogenization of the Signorini boundary-value problem in a thick junction and boundary integral equations for the homogenized problem”, Math. Meth. Appl. Sci, 2010, n/a
Sango M., “Homogenization of the Neumann Problem for a Quasilinear Elliptic Equation in a Perforated Domain”, Networks and Heterogeneous Media, 5:2 (2010), 361–384
Kazmerchuk Yu.A., Mel'nyk T.A., “Homogenization of the signorini boundary-value problem in a thick plane junction”, Nonlinear Oscill., 12:1 (2009), 45–59
G. V. Sandrakov, “Homogenization of variational inequalities for non-linear diffusion problems in perforated domains”, Izv. Math., 69:5 (2005), 1035–1059
I. I. Argatov, “Osrednenie smeshannoi zadachi dlya operatora Laplasa s usloviyami Sinorini na vnutrennei melkozernistoi granitse”, Sib. zhurn. industr. matem., 7:4 (2004), 3–15
Sandrakov G.V., “Homogenization of variational inequalities with the Signorini condition in perforated domains”, Dokl. Math., 70:3 (2004), 941–944
Pastukhova S.E., “The oscillating boundary phenomenon in the homogenization of a climatization problem”, Differ. Equ., 37:9 (2001), 1276—-1283
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