On the homogenization of the Poisson equation in partially perforated domains with arbitrary density of cavities and mixed type conditions on their boundary

Olga A. Oleinik; Tatiana A. Shaposhnikova

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1996)

  • Volume: 7, Issue: 3, page 129-146
  • ISSN: 1120-6330

Abstract

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In this paper we study the behavior of solutions of the boundary value problem for the Poisson equation in a partially perforated domain with arbitrary density of cavities and mixed type conditions on their boundary. The corresponding spectral problem is also considered. A short communication of similar results can be found in [1].

How to cite

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Oleinik, Olga A., and Shaposhnikova, Tatiana A.. "On the homogenization of the Poisson equation in partially perforated domains with arbitrary density of cavities and mixed type conditions on their boundary." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 7.3 (1996): 129-146. <http://eudml.org/doc/244232>.

@article{Oleinik1996,
abstract = {In this paper we study the behavior of solutions of the boundary value problem for the Poisson equation in a partially perforated domain with arbitrary density of cavities and mixed type conditions on their boundary. The corresponding spectral problem is also considered. A short communication of similar results can be found in [1].},
author = {Oleinik, Olga A., Shaposhnikova, Tatiana A.},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Homogenization; Poisson equation; Perforated domains; Mixed type conditions; Spectral problem; spectrum of a sequence of singular perturbed operators},
language = {eng},
month = {12},
number = {3},
pages = {129-146},
publisher = {Accademia Nazionale dei Lincei},
title = {On the homogenization of the Poisson equation in partially perforated domains with arbitrary density of cavities and mixed type conditions on their boundary},
url = {http://eudml.org/doc/244232},
volume = {7},
year = {1996},
}

TY - JOUR
AU - Oleinik, Olga A.
AU - Shaposhnikova, Tatiana A.
TI - On the homogenization of the Poisson equation in partially perforated domains with arbitrary density of cavities and mixed type conditions on their boundary
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1996/12//
PB - Accademia Nazionale dei Lincei
VL - 7
IS - 3
SP - 129
EP - 146
AB - In this paper we study the behavior of solutions of the boundary value problem for the Poisson equation in a partially perforated domain with arbitrary density of cavities and mixed type conditions on their boundary. The corresponding spectral problem is also considered. A short communication of similar results can be found in [1].
LA - eng
KW - Homogenization; Poisson equation; Perforated domains; Mixed type conditions; Spectral problem; spectrum of a sequence of singular perturbed operators
UR - http://eudml.org/doc/244232
ER -

References

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  1. OLEINIK, O. A. - SHAPOSHNIKOVA, T. A., On homogenization problems in partially perforated domains. Russian Math. Survey, vol. 50, n. 4, 1995. 
  2. JÄGER, W. - OLEINIK, O. A. - SHAMAEV, A. S., On a homogenization problem for the Laplace operator in a partially perforated domain with the Neumann condition on holes. Preprint 93-53, Heidelberg, Inter-Dissiplinäres Zentrum for Wissenschaftliches Rechnen, Heidelberg1993. 
  3. JÄGER, W. - OLEINIK, O. A. - SHAMAEV, A. S., On homogenization problem for the Laplace operator in partially perforated domain. Doklady RAS, vol. 333, 4, 1993, 424-427. Zbl0923.35022MR1260777
  4. OLEINIK, O. A. - SHAPOSHNIKOVA, T. A., On homogenization of solutions of the Dirichlet problem in partially perforated domains of the general form with the nonperiodic structure. Vestnik of Mosk. University, ser. Math, and Mech., n. 2, 1995, 49-55. Zbl0872.35011MR1376568
  5. OLEINIK, O. A. - SHAPOSHNIKOVA, T. A., On an approach of constructing of approximations in homogenization problems for partially perforated domains. Diff. Equations, vol. 30, n. 11, 1994, 1994-1999. Zbl0854.35010MR1348290
  6. OLEINIK, O. A. - SHAPOSHNIKOVA, T. A., On the homogenization problem in partially perforated domains with the mixed type conditions, containing a small parameter, on the boundary of cavities. Diff. Equations, n. 7, 1995. Zbl0870.35012MR1363782
  7. OLEINIK, O. A. - SHAMAEV, A. S., On homogenization of solutions of the Laplace equation in partially perforated domains with the Dirichlet condition on the boundary of cavities. Doklady RAS, vol. 337, n. 2, 1994, 168-171. Zbl0848.35008MR1301632
  8. OLEINIK, O. A. - SHAPOSHNIKOVA, T. A., On homogeneization problems for the Laplace operator in partially perforated domains with Neumann's condition on the boundary of cavities. Rend. Mat. Acc. Lincei, s. 9, v. 6, 1995, 133-142. Zbl0848.35009MR1363782
  9. JÄGER, W. - MIKELIC, A., A study of a contact between porous media and ordinary media for the case of the Laplace equation. Preprint, University of Heidelberg, 1993. 
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