Interaction of concentrated masses in a harmonically oscillating spatial body with Neumann boundary conditions

 Access to full text

 Full (PDF)

1. [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. Zbl0542.73006MR755735
2. [2] E. SANCHEZ-PALENCIA, H. TCHTAT, 1984, Vibration de systèmes élastiques avec masses concentrées, Rend. Sem. Mat. Univ. Politec. Torino, 42, 43-63. Zbl0658.73044MR834781
3. [3] C. LEAL, J. SANCHEZ-HUBERT, 1989, Perturbation of the eigenvalues of a membrane with concentrated mass. Quart. Appl. Math., vol. 47, 93-103. Zbl0685.73025MR987898
4. [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. Zbl0728.35077MR1097888
5. [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. Zbl0698.70003MR996423
6. [6] O. A. OLEINIK, G. A. YOSIFIAN, A. S. SHAMAEV, 1990, Mathematical Problems in Theory of Non-Homogeneous Media, Moscow : Izdat. Moskov. Universiteta. Zbl0768.73003
7. [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). Zbl0491.35013MR658154
8. [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. [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). Zbl0599.35056
10. [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). Zbl0618.35005MR837128
11. [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). Zbl0701.35021MR1010835
12. [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). Zbl0162.16301MR226187
13. [13] S. A. NAZAROV, B. A. PLAMENEVSKII, 1991, Elliptic Problems in Domainswith Piecewise Smooth Boundaries, Moscow : Nauka (Russian). 
14. [14] S. A. NAZAROV, 1989, On the Sanchez-Palencia problem with the Neumann boundary conditions, Izvestija VUZ. Matem. No. 11, 60-66 (Russian). Zbl0801.35092MR1045104
15. [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.). Zbl0181.13504