EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 48 / No 5 (September-October 2014) ESAIM: M2AN, 48 5 (2014) 1495-1528 References
Free Access
Issue
ESAIM: M2AN
Volume 48, Number 5, September-October 2014
Page(s) 1495 - 1528
DOI https://doi.org/10.1051/m2an/2014007
Published online 13 August 2014
  1. A.A. Arsen’ev, The existence of resonance poles and resonances under scattering in the case of boundary conditions of the second and third kind.Ž. Vyčisl. Mat. i Mat. Fiz. 16 (1976) 718–724. [Google Scholar]
  2. J. Beale, Thomas Scattering frequencies of reasonators. Commun. Pure Appl. Math. 26 (1973) 549–563. [CrossRef] [MathSciNet] [Google Scholar]
  3. L. Berlyand, G. Cardone, Y. Gorb and G.P. Panasenko, Asymptotic analysis of an array of closely spaced absolutely conductive inclusions. Netw. Heterog. Media 1 (2006) 353–377. [CrossRef] [MathSciNet] [Google Scholar]
  4. D. Blanchard, A. Gaudiello and G. Griso, Junction of a periodic family of elastic rods with a 3d plate. I. J. Math. Pures Appl. 88 (2007) 1–33. [CrossRef] [MathSciNet] [Google Scholar]
  5. D. Blanchard, A. Gaudiello and G. Griso, Junction of a periodic family of elastic rods with a thin plate. II. J. Math. Pures Appl. 88 (2007) 149–190. [CrossRef] [Google Scholar]
  6. D. Blanchard and G. Griso, Microscopic effects in the homogenization of the junction of rods and a thin plate. Asymptot. Anal. 56 (2008) 1–36. [MathSciNet] [Google Scholar]
  7. D. Blanchard and G. Griso, Asymptotic behavior of a structure made by a plate and a straight rod. Chin. Annal. Math. Ser. B 34 (2013) 399–434. [CrossRef] [Google Scholar]
  8. D. Borisov, R. Bunoiu and G. Cardone, On a waveguide with frequently alternating boundary conditions: homogenized Neumann condition. Annal. Henri Poincaré 11 (2010) 1591–1627. [CrossRef] [Google Scholar]
  9. D. Borisov, R. Bunoiu and G. Cardone, Homogenization and asymptotics for a waveguide with an infinite number of closely located small windows. J. Math. Sci. 176 (2011) 774–785. [CrossRef] [MathSciNet] [Google Scholar]
  10. D. Borisov and R. Bunoiu, Cardone G., On a waveguide with an infinite number of small windows. C. R. Math. Acad. Sci. Paris, Ser. I 349 (2011) 53–56. [CrossRef] [Google Scholar]
  11. D. Borisov, R. Bunoiu and G. Cardone, Waveguide with non-periodically alternating Dirichlet and Robin conditions: homogenization and asymptotics. Z. Angew. Math. Phys. 64 (2013) 439–472. [CrossRef] [MathSciNet] [Google Scholar]
  12. D. Borisov and G. Cardone, Homogenization of the planar waveguide with frequently alternating boundary conditions. J. Phys. A: Math. Theor. 42 (2009) 365–205. [CrossRef] [Google Scholar]
  13. D. Borisov and G. Cardone, Complete asymptotic expansions for the eigenvalues of the Dirichlet Laplacian in thin three-dimensional rods. ESAIM: COCV 17 (2011) 887–908. [CrossRef] [EDP Sciences] [Google Scholar]
  14. D. Borisov and G. Cardone, Planar Waveguide with “Twisted” Boundary Conditions: Small Width. J. Math. Phys. 53 (2012) 023–503. [CrossRef] [Google Scholar]
  15. D. Borisov, G. Cardone, L. Faella and C. Perugia, Uniform resolvent convergence for strip with fast oscillating boundary. J. Differ. Eqs. 255 (2013) 4378–4402. [CrossRef] [Google Scholar]
  16. G. Cardone, A. Corbo Esposito and G.P. Panasenko, Asymptotic partial decomposition for diffusion with sorption in thin structures. Nonlinear Anal. 65 (2006) 79–106. [CrossRef] [MathSciNet] [Google Scholar]
  17. G. Cardone, A. Corbo Esposito and S.E. Pastukhova, Homogenization of a scalar problem for a combined structure with singular or thin reinforcement. Z. Anal. Anwend. 26 (2007) 277–301. [MathSciNet] [Google Scholar]
  18. G. Cardone, R. Fares and G.P. Panasenko, Asymptotic expansion of the solution of the steady Stokes equation with variable viscosity in a two-dimensional tube structure. J. Math. Phys. 53 (2012) 103–702. [CrossRef] [Google Scholar]
  19. G. Cardone, G.P. Panasenko and Y. Sirakov, Asymptotic analysis and numerical modeling of mass transport in tubular structures. Math. Models Methods Appl. Sci. 20 (2010) 397–421. [CrossRef] [Google Scholar]
  20. G. Cardone, S.A. Nazarov and A.L. Piatnitski, On the rate of convergence for perforated plates with a small interior Dirichlet zone. Z. Angew. Math. Phys. 62 (2011) 439–468. [CrossRef] [MathSciNet] [Google Scholar]
  21. P.G. Ciarlet, Mathematical elasticity. Vol. II. Theory of plates. Studies Math. Appl. 27 (1997). [Google Scholar]
  22. D. Cioranescu, O.A. Oleĭnik and G. Tronel, Korn’s inequalities for frame type structures and junctions with sharp estimates for the constants. Asymptot. Anal. 8 (1994) 1–14. [Google Scholar]
  23. D. Cioranescu and J. Saint Jean Paulin, Homogenization of reticulated structures. Appl. Math. Sci. 136 (1999). [CrossRef] [Google Scholar]
  24. R.R. Gadyl’shin, On the eigenvalues of a dumbbell with a thin handle. Izv. Ross. Akad. Nauk Ser. Mat. 69 (2005) 45–110; Izv. Math. 69 (2005) 265–329. [CrossRef] [MathSciNet] [Google Scholar]
  25. A. Gaudiello, R. Monneau, J. Mossino, F. Murat and A. Sili, Junction of elastic plates and beams. ESAIM: COCV 13 (2007) 419–457. [CrossRef] [EDP Sciences] [Google Scholar]
  26. A. Gaudiello and A. Sili, Asymptotic analysis of the eigenvalues of a Laplacian problem in a thin multidomain. Indiana Univ. Math. J. 56 (2007) 1675–1710. [CrossRef] [MathSciNet] [Google Scholar]
  27. A. Gaudiello and A. Sili, Asymptotic analysis of the eigenvalues of an elliptic problem in an anisotropic thin multidomain. Proc. Roy. Soc. Edinburgh Sect. A 141 (2011) 739–754. [CrossRef] [MathSciNet] [Google Scholar]
  28. I. Gruais, Modélisation de la jonction entre une plaque et une poutre en élasticité linéarisée. RAIRO Modél. Math. Anal. Numér. 27 (1993) 77–105. [MathSciNet] [Google Scholar]
  29. I. Gruais, Modeling of the junction between a plate and a rod in nonlinear elasticity. Asymptot. Anal. 7 (1993) 179–194. [Google Scholar]
  30. A.M. Il’in, A boundary value problem for an elliptic equation of second order in a domain with a narrow slit. I. The two-dimensional case. Mat. Sb. 99 (1976) 514–537. [Google Scholar]
  31. Il’in A.M., Matching of asymptotic expansions of solutions of boundary value problems. Moscow, Nauka (1989); Translations: Math. Monogr., vol. 102. AMS, Providence (1992). [Google Scholar]
  32. P. Joly and S. Tordeux. Matching of asymptotic expansions for waves propagation in media with thin slots II: The error estimates. ESAIM: M2AN 42 (2008) 193–221. [CrossRef] [EDP Sciences] [Google Scholar]
  33. V.A. Kondratiev, Boundary problems for elliptic equations in domains with conical or angular points. Trudy Moskov. Mat. Obshch. 16 (1967) 209−292; Trans. Moscow Math. Soc. 16 (1967) 227−313. [Google Scholar]
  34. V. Kozlov, V. Maz’ya and A. Movchan, Asymptotic analysis of fields in multi-structures. Oxford Math. Monogr. Oxford University Press (1999). [Google Scholar]
  35. V.A. Kozlov, V.G. Maz’ya and A.B. Movchan, Asymptotic analysis of a mixed boundary value problem in a multi-structure. Asymptot. Anal. 8 (1994) 105–143. [Google Scholar]
  36. V.A. Kozlov, V.G. Maz’ya and A.B. Movchan, Asymptotic representation of elastic fields in a multi-structure. Asymptot. Anal. 11 (1995) 343–415. [Google Scholar]
  37. V.A. Kozlov, V.G. Maz’ya and A.B. Movchan, Fields in non-degenerate 1D-3D elastic multi-structures. Quart. J. Mech. Appl. Math. 54 (2001) 177–212. [CrossRef] [MathSciNet] [Google Scholar]
  38. O.A. Ladyzhenskaya, The boundary value problems of mathematical physics. Moscow, Nauka (1973); Appl. Math. Sci., vol. 49. Springer-Verlag, New York (1985). [Google Scholar]
  39. N.S. Landkof, Foundations of modern potential theory. Die Grundlehren der mathematischen Wissenschaften, vol. 180. Springer-Verlag, New York-Heidelberg (1972). [Google Scholar]
  40. H. Le Dret, Problèmes variationnels dans le multi-domaines: modélisation des jonctions et applications. Res. Appl. Math., vol. 19. Masson, Paris (1991). [Google Scholar]
  41. D. Leguillon and E. Sanchez-Palencia, Approximation of a two-dimensional problem of junction. Comput. Mech. 6 (1990) 435–455. [CrossRef] [Google Scholar]
  42. J.L. Lions, Magenes E., Non-homogeneous boundary value problems and applications. Springer-Verlag, New York-Heidelberg (1972). [Google Scholar]
  43. J.-L. Lions, Some more remarks on boundary value problems and junctions. Proc. of Asymptotic methods for elastic structures, Lisbon 1993. De Gruyter, Berlin (1995) 103–118. [Google Scholar]
  44. V.G. Maz’ya, S.A. Nazarov and B.A. Plamenevskij, Asymptotic theory of elliptic boundary value problems in singularly perturbed domains, Tbilisi Univ. 1981; Operator Theory. Adv. Appl., vol. 112. Birkhäuser, Basel (2000). [Google Scholar]
  45. S.A. Nazarov, Asymptotic Theory of Thin Plates and Rods. Dimension Reduction and Integral Estimates, vol. 1. Nauchnaya Kniga, Novosibirsk (2001). [Google Scholar]
  46. S.A. Nazarov, Selfadjoint extensions of the operator of the Dirichlet problem in weighted function spaces. Mat. Sb. 137 (1988) 224–241; Math. USSR-Sb. 65 (1990) 229–247. [Google Scholar]
  47. S.A. Nazarov, Asymptotic behavior of the solution of a boundary value problem in a thin cylinder with a nonsmooth lateral surface. Izv. Ross. Akad. Nauk Ser. Mat. 57 (1993) 202–239; Russian Acad. Sci. Izv. Math. 42 (1994) 183–217. [Google Scholar]
  48. S.A. Nazarov, Junctions of singularly degenerating domains with different limit dimensions. I. Tr. Semin. im. I. G. Petrovskogo 18 (1995) 3–78; J. Math. Sci. 80 (1996) 1989–2034. [Google Scholar]
  49. S.A. Nazarov, Korn’s inequalities for junctions of bodies and thin rods. Math. Meth. Appl. Sci. 20 (1997) 219–243. [CrossRef] [Google Scholar]
  50. S.A. Nazarov, Asymptotic conditions at a point, selfadjoint extensions of operators, and the method of matched asymptotic expansions. Proc. St. Petersburg Math. Society, V, 77–125; Amer. Math. Soc. Transl. Ser. 2, 193, Amer. Math. Soc., Providence (1999). [Google Scholar]
  51. S.A. Nazarov, Asymptotic expansions at infinity of solutions of a problem in the theory of elasticity in a layer. Tr. Mosk. Mat. Obs. 60 (1999) 3–97; Trans. Moscow Math. Soc. (1999) 1–85. [Google Scholar]
  52. S.A. Nazarov, Junctions of singularly degenerating domains with different limit dimensions. II. Tr. Semin. im. I. G. Petrovskogo 20 (2000) 155–195; 312–313; J. Math. Sci. 97 (1999) 155–195. [Google Scholar]
  53. S.A. Nazarov, Asymptotic analysis and modeling of the junction of a massive body and thin rods. Tr. Semin. im. I. G. Petrovskogo 24 (2004) 95–214, 342–343; J. Math. Sci. 127 (2005) 2192–2262. [Google Scholar]
  54. S.A. Nazarov, Estimates for the accuracy of modeling boundary value problems on the junction of domains with different limit dimensions. Izv. Ross. Akad. Nauk Ser. Mat. 68 (2004) 119–156; Izv. Math. 68 (2004) 1179–1215. [CrossRef] [MathSciNet] [Google Scholar]
  55. S.A. Nazarov, Elliptic boundary value problems on hybrid domains. Funktsional. Anal. i Prilozhen 38 (2004) 55–72; Funct. Anal. Appl. 38 (2004) 283–297. [CrossRef] [MathSciNet] [Google Scholar]
  56. S.A. Nazarov, Korn’s inequalities for elastic joints of massive bodies, thin plates, and rods. Uspekhi Mat. Nauk 63 (2008) 379, 37–110; Russian Math. Surveys 63 (2008) 35–107. [CrossRef] [Google Scholar]
  57. S.A. Nazarov, Asymptotic behavior of the solutions of the spectral problem of the theory of elasticity for a three-dimensional body with a thin coupler. Sibirsk. Mat. Zh. 53 (2012) 345–364; Sib. Math. J. 53 (2012) 274–290. [CrossRef] [Google Scholar]
  58. S.A. Nazarov and B.A. Plamenevsky, Elliptic problems in domains with piecewise smooth boundaries. Moscow: Nauka. (1991); de Gruyter Expositions Math., vol. 13. Walter de Gruyter & Co., Berlin (1994). [Google Scholar]
  59. G.P. Panasenko, Multi-scale Modeling for Structures and Composites. Springer, Dordrecht (2005). [Google Scholar]
  60. G. Pólya and G. Szegö, Isoperimetric Inequalities in Mathematical Physics, Annal. Math. Studies, vol. 27, Princeton University Press, Princeton (1951). [Google Scholar]
  61. J. Sanchez-Hubert, Sanchez-Palencia E., Coques élastiques minces. Propriétés asymptotiques. Recherches en Mathématiques Appliquées. Paris, Masson (1997). [Google Scholar]
  62. V.I. Smirnov, A course of higher mathematics. Advanced calculus, vol. II. Sneddon Pergamon Press, London (1964). [Google Scholar]
  63. V.I. Smirnov, A course of higher mathematics. Integral equations and partial differential equations, vol. IV. Sneddon Pergamon Press, London (1964). [Google Scholar]
  64. M. Van Dyke, Perturbation methods in fluid mechanics. Appl. Math. Mech., vol. 8 Academic Press, New York, London (1964). [Google Scholar]
  65. V.S. Vladimirov, Generalized Functions in Mathematical Physics, Mir Moscow (1979). [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.

Recommended for you