Interaction of concentrated masses in a harmonically oscillating spatial body with Neumann boundary conditions
Nazarov, S. A.
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 27 (1993), p. 777-799 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1993-01-01
@article{M2AN_1993__27_6_777_0,
     author = {Nazarov, S. A.},
     title = {Interaction of concentrated masses in a harmonically oscillating spatial body with Neumann boundary conditions},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {27},
     year = {1993},
     pages = {777-799},
     mrnumber = {1246999},
     zbl = {0791.35090},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1993__27_6_777_0}
}

Nazarov, S. A. Interaction of concentrated masses in a harmonically oscillating spatial body with Neumann boundary conditions. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 27 (1993) pp. 777-799. http://gdmltest.u-ga.fr/item/M2AN_1993__27_6_777_0/

[1] E. Sanchez-Palencia, 1984, Perturbation of Eigenvalues in Thermoelasticity and Vibration of Systems with Concentrated Masses, Lecture Notes in Physics,195, Berlin, Heidelberg, New York : Springer, 346-368. | MR 755735 | Zbl 0542.73006

[2] E. Sanchez-Palencia, H. Tchtat, 1984, Vibration de systèmes élastiques avec masses concentrées, Rend. Sem. Mat. Univ. Politec. Torino, 42, 43-63. | MR 834781 | Zbl 0658.73044

[3] C. Leal, J. Sanchez-Hubert, 1989, Perturbation of the eigenvalues of a membrane with concentrated mass. Quart. Appl. Math., vol. 47, 93-103. | MR 987898 | Zbl 0685.73025

[4] U. A. Golovatii, S. A. Nazarov, O. A. Oleinik, 1990, Asymptotic decompositions of eigenvalues and eigenfunctins of problems on oscillating media with concentrated masses, Trudy Mat. inst. A.N S.S.S.R., 192, 42-60. | MR 1097888 | Zbl 0728.35077

[5] J. Sanchez-Hubert, E. Sanchez-Palencia, 1989, Vibration and Coupling of Continuous Systems Asymptotic Methods, Berlin, Heidelberg, New York, London, Paris, Tokyo : Springer-Verlag. | MR 996423 | Zbl 0698.70003

[6] O. A. Oleinik, G. A. Yosifian, A. S. Shamaev, 1990, Mathematical Problems in Theory of Non-Homogeneous Media, Moscow : Izdat. Moskov. Universiteta.

[7] V. G. Maz'Ya, S. A. Nazarov, B. A. Plamenevskii, 1981, On the asymptotics of solutions of elliptic boundary value problems in domains perturbed irregularly, Probl. mat. anal., 8, Leningrad : izdat. Leningrad Universiteta, 72-153 (Russian). | MR 658154 | Zbl 0491.35013

[8] W. G. Mazja, S. A. Nasarow, B. A. Plamenewski, 1990, Asymptotische Theorie elliptischer Randwertaufgaben in singulär gestörten Gebieten, Bd. 1, Berlin : Akademie-Verlag.

[9] V. G. Maz'Ya, S. A. Nazarov, B. A. Plameenvskii, 1983, On the singularities of solutions of the Dirichlet problem in the exterior of a slender cone, Matem. Sbornik, 122, 435-436 (Russian ; English transl. (1987) in Math. USSR Sbornik, 57, 317-349). | Zbl 0599.35056

[10] S. A. Nazarov, 1986, Justification of asymptotic expansions of the eigenvalues of nonselfadjoint singularly perturbed elliptic boundary value problems, Matem.sbornik, 129, 307-337 (Russian ; English transl. (1987) in Math. USSR Sbornik,57, 317-349). | MR 837128 | Zbl 0618.35005

[11] V. G. Maz'Ya, S. A. Nazarov, 1989, On the singularities of solutions of the Neumann problem at a conical point, Sibirsk. Matem. Zh., 30, 52-63 (Russian). | MR 1010835 | Zbl 0701.35021

[12] V. A. Kondrat'Ev, 1967, Boundary value problems for elliptic equations in domains with conical or angular points, Trudy Mat. Obshch., 16, 209-292 (Russian ; English transl. (1967) in Trans. Moscow Math. Soc., 16). | MR 226187 | Zbl 0194.13405 | Zbl 0162.16301

[13] S. A. Nazarov, B. A. Plamenevskii, 1991, Elliptic Problems in Domainswith Piecewise Smooth Boundaries, Moscow : Nauka (Russian).

[14] S. A. Nazarov, 1989, On the Sanchez-Palencia problem with the Neumann boundary conditions, Izvestija VUZ. Matem. No. 11, 60-66 (Russian). | MR 1045104 | Zbl 0801.35092

[15] I. C. Gogberg, M. G. Krein, 1965, Introduction to the theory of linear nonselfadjoint operators in Hilbert space, Moscow : Nauka (Russian ; English transl. (1969). Amer. Math. Soc., Providence, R.I.). | Zbl 0181.13504