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Homogenizaton of a Nonhomogeneous Signorini Problem for the Poisson Equation in a Periodically Perforated Domain

Homogenizaton of a Nonhomogeneous Signorini Problem for the Poisson Equation in a Periodically... Differential Equations, Vol. 39, No. 3, 2003, pp. 387–396. Translated from Differentsial'nye Uravneniya, Vol. 39, No. 3, 2003, pp. 359–366. Original Russian Text Copyright c 2003 by Vorob'ev, Shaposhnikova. PARTIAL DIFFERENTIAL EQUATIONS Homogenizaton of a Nonhomogeneous Signorini Problem for the Poisson Equation in a Periodically Perforated Domain A. Yu. Vorob'ev and T. A. Shaposhnikova Moscow State University, Moscow, Russia Received December 5, 2001 Numerous papers (e.g., see [1{4]) deal with homogenization problems for variational inequalities. In the present paper, we study the asymptotic behavior of solutions of the Poisson equation in an "-periodically perforated domain with nonzero Signorini conditions on the cavity boundaries as " ! 0. Let be a smooth bounded domain in R , n  3, with boundary @ . By Q = fx 2 R ; 0 <x < 1;j =1;:::;ng we denote the unit cube in R .Let G be a domain in Q such that G  Q is di eomorphic to a 0 0 ball and let T = a G . " " 0 Suppose that n1 n lim a " = C =const > 0: (1) "!0 We set Y = "QnT ,! = Y + "z , \ ! http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Homogenizaton of a Nonhomogeneous Signorini Problem for the Poisson Equation in a Periodically Perforated Domain

Vorob'ev, A.; Shaposhnikova, T.
Differential Equations , Volume 39 (3) – Oct 5, 2004
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References (2)

Publisher
Springer Journals
Copyright
Copyright © 2003 by MAIK “Nauka/Interperiodica”
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1023/A:1026025902733
Publisher site
See Article on Publisher Site

Abstract

Differential Equations, Vol. 39, No. 3, 2003, pp. 387–396. Translated from Differentsial'nye Uravneniya, Vol. 39, No. 3, 2003, pp. 359–366. Original Russian Text Copyright c 2003 by Vorob'ev, Shaposhnikova. PARTIAL DIFFERENTIAL EQUATIONS Homogenizaton of a Nonhomogeneous Signorini Problem for the Poisson Equation in a Periodically Perforated Domain A. Yu. Vorob'ev and T. A. Shaposhnikova Moscow State University, Moscow, Russia Received December 5, 2001 Numerous papers (e.g., see [1{4]) deal with homogenization problems for variational inequalities. In the present paper, we study the asymptotic behavior of solutions of the Poisson equation in an "-periodically perforated domain with nonzero Signorini conditions on the cavity boundaries as " ! 0. Let be a smooth bounded domain in R , n  3, with boundary @ . By Q = fx 2 R ; 0 <x < 1;j =1;:::;ng we denote the unit cube in R .Let G be a domain in Q such that G  Q is di eomorphic to a 0 0 ball and let T = a G . " " 0 Suppose that n1 n lim a " = C =const > 0: (1) "!0 We set Y = "QnT ,! = Y + "z , \ !

Journal

Differential Equations – Springer Journals

Published: Oct 5, 2004

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