Asymptotically sharp uniform estimates in a scalar spectral stiff problem

Comptes Rendus - Mecanique

Volumn 331, Issue 5, 2003, Pages 325-330

  Lobo, Miguel ^a   Nazarov, Serguei A ^b   Pérez, Eugenia ^a  

^a UNIVERSITY OF CANTABRIA   (Spain)

^b INSTITUTE OF PROBLEMS OF MECHANICAL ENGINEERING   (Russian Federation)

Author keywords

Acoustics; Low frequencies; Middle frequencies; Spectral analysis; Stiff problem; Vibrations; Waves

Indexed keywords

STIFFNESS;

ACOUSTICS; ARTICLE; FREQUENCY ANALYSIS; MATHEMATICAL ANALYSIS; RIGIDITY; SPECTROSCOPY; VIBRATION; WAVEFORM;

EID: 0038237071     PISSN: 16310721     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1631-0721(03)00073-1     Document Type: Article

References (9)

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2. M. Lobo, E. Pérez, High frequency viabrations in a stiff problem, Math. Models Methods Appl. Sci. 7 (2) (1997) 291-311.
3. G.P. Panasenko, Asymptotics of solutions and eigenvalues of elliptic equations with strongly variable coefficients, Dokl. Akad. Nauk 252 (6) (1980) 1320-1325. English transl.: Soviet Math. Dokl. 21 (1980) 942-947.
4. G.P. Panasenko, Asymptotics of the eigenvalues of elliptic equations with strongly varying coefficients, Trudy Sem. Petrovsk. 12 (1987) 201-217.
5. M. Lobo, S.A. Nazarov, E. Pérez, Eigenoscillations of contrastly non-homogeneous elastic body. Asymptotic and uniform estimates for the eigenvalues, in preparation.
6. É. Sanchez-Palencia, Asymptotic and spectral properites of a class of singular-stiff problems, J. Math. Pures Appl. 71 (1992) 379-406.
7. J. Sanchez-Hubert, É. Sanchez-Palencia, Vibration and Coupling of Continuous Systems. Asymptotic Methods, Springer-Verlag, Heidelberg, 1989.
8. S.A. Nazarov, Asymptotic Theory of Thin Plates and Rods. Vol. 1. Dimension Reduction and Integral Estimates, Nauchnaya Kniga, Novosibirck, 2002.
9. S.A. Nazarov, Estimating the convergence rate for eigenfrequences of anisotropic plates with variable thickness, C. R. Mecanique 330 (2002) 603-607.