Free Access
Issue
ESAIM: COCV
Volume 18, Number 2, April-June 2012
Page(s) 583 - 610
DOI https://doi.org/10.1051/cocv/2011107
Published online 26 August 2011
  1. D. Blanchard and A. Gaudiello, Homogenization of highly oscillating boundaries and reduction of dimension for a monotone problem. ESAIM : COCV 9 (2003) 449–460. [Google Scholar]
  2. D. Blanchard, A. Gaudiello and G. Griso, Junction of a periodic family of elastic rods with 3d plate. Part I. J. Math. Pures Appl. 88 (2007) 1–33 (Part I); 88 (2007) 149–190 (Part II). [CrossRef] [MathSciNet] [Google Scholar]
  3. D. Blanchard, A. Gaudiello and T.A. Mel’nyk, Boundary homogenization and reduction of dimention in a Kirchhoff-Love plate. SIAM J. Math. Anal. 39 (2008) 1764–1787. [CrossRef] [MathSciNet] [Google Scholar]
  4. G. Buttazzo, Γ-convergence and its applications to some problem in the calculus of variations, in School on Homogenization, ICTP, Trieste, 1993 (1994) 38–61. [Google Scholar]
  5. G. Buttazzo and G. Dal Maso, Γ-convergence and optimal control problems. J. Optim. Theory Appl. 38 (1982) 385–407. [CrossRef] [MathSciNet] [Google Scholar]
  6. G.A. Chechkin, T.P. Chechkina, C. D’Apice, U. De-Maio and T.A. Mel’nyk, Asymptotic analysis of a boundary value problem in a cascade thick junction with a random transmission zone. Appl. Anal. 88 (2009) 1543–1562. [CrossRef] [MathSciNet] [Google Scholar]
  7. U. De Maio, A. Gaudiello and C. Lefter, optimal control for a parabolic problem in a domain with highly oscillating boundary. Appl. Anal. 83 (2004) 1245–1264. [CrossRef] [MathSciNet] [Google Scholar]
  8. U. De Maio, T. Durante and T.A. Mel’nyk, Asymptotic approximation for the solution to the Robin problem in a thick multi-level junction. Math. Models Methods Appl. Sci. 15 (2005) 1897–1921. [CrossRef] [MathSciNet] [Google Scholar]
  9. Z. Denkowski and S. Mortola, Asymptotic behavior of optimal solutions to control problems for systems described by differential inclusions corresponding to partial differential equations. J. Optim. Theory Appl. 78 (1993) 365–391. [CrossRef] [MathSciNet] [Google Scholar]
  10. T. Durante and T.A. Mel’nyk, Asymptotic analysis of an optimal control problem involving a thick two-level junction with alternate type of controls. J. Optim. Theory Appl. 144 (2010) 205–225. [CrossRef] [MathSciNet] [Google Scholar]
  11. T. Durante, L. Faella and C. Perugia, Homogenization and behaviour of optimal controls for the wave equation in domains with oscillating boundary. Nonlinear Differ. Equ. Appl. 14 (2007) 455–489. [CrossRef] [Google Scholar]
  12. S. Kesavan and J. Saint Jean Paulin, Optimal control on perforated domains. J. Math. Anal. Appl. 229 (1999) 563–586. [CrossRef] [MathSciNet] [Google Scholar]
  13. Y.I. Lavrentovich, T.V. Knyzkova and V.V. Pidlisnyuk, The potential of application of new nanostructural materials for degradation of pesticides in water, in Proceedings of the 7th Int. HCH and Pesticides Forum Towards the establishment of an obsolete POPS/pecticides stockpile fund for Central and Eastern European countries and new independent states, Kyiv, Ukraine (2003) 167–169. [Google Scholar]
  14. M. Lenczner, Multiscale model for atomic force microscope array mechanical behavior. Appl. Phys. Lett. 90 (2007) 091908; doi : 10.1063/1.2710001. [CrossRef] [Google Scholar]
  15. J.L. Lions, Optimal Control of Systems Governed by Partial Differential Equations. Springer-Verlag, Berlin (1971). [Google Scholar]
  16. S.E. Lyshevshi, Mems and Nems : Systems, Devices, and Structures. CRC Press, Boca Raton, FL (2002). [Google Scholar]
  17. T.A. Mel’nyk, Homogenization of the Poisson equation in a thick periodic junction. Z. f. Anal. Anwendungen 18 (1999) 953–975. [CrossRef] [Google Scholar]
  18. T.A. Mel’nyk, Homogenization of a perturbed parabolic problem in a thick periodic junction of type 3 : 2 : 1. Ukr. Math. J. 52 (2000) 1737–1749. [CrossRef] [Google Scholar]
  19. T.A. Mel’nyk, Homogenization of a boundary-value problem with a nonlinear boundary condition in a thick junction of type 3 : 2 : 1. Math. Models Meth. Appl. Sci. 31 (2008) 1005–1027. [CrossRef] [Google Scholar]
  20. T.A. Mel’nyk and G.A. Chechkin, Asymptotic analysis of boundary value problems in thick three-dimensional multi-level junctions. Math. Sb. 200 3 (2009) 49–74 (in Russian); English transl. : Sb. Math. 200 (2009) 357–383. [CrossRef] [Google Scholar]
  21. T.A. Mel’nyk and S.A. Nazarov, Asymptotic structure of the spectrum in the problem of harmonic oscillations of a hub with heavy spokes. Dokl. Akad. Nauk Russia 333 (1993) 13–15 (in Russian); English transl. : Russian Acad. Sci. Dokl. Math. 48 (1994) 28–32. [Google Scholar]
  22. T.A. Mel’nyk and S.A. Nazarov, Asymptotic structure of the spectrum of the Neumann problem in a thin comb-like domain. C.R. Acad Sci. Paris, Ser. 1 319 (1994) 1343–1348. [Google Scholar]
  23. T.A. Mel’nyk and S.A. Nazarov, Asymptotics of the Neumann spectral problem solution in a domain of thick comb type. Trudy Seminara imeni I.G. Petrovskogo 19 (1996) 138–173 (in Russian); English transl. : J. Math. Sci. 85 (1997) 2326–2346. [Google Scholar]
  24. T.A. Mel’nyk and D. Yu. Sadovyj, Homogenization of elliptic problems with alternating boundary conditions in a thick two-level junction of type 3 :2 :2. J. Math. Sci. 165 (2010) 67–90. [Google Scholar]
  25. T.A. Mel’nyk, Iu.A. Nakvasiuk and 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. 34 (2011) 758–775. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.