Aslanyan, A. G.; Vasil’ev, D. G.; Lidskij, V. B. Frequencies of free vibrations of a thin shell interacting with a liquid. (English) Zbl 0576.73039 Funct. Anal. Appl. 15, 157-163 (1982). Translation from Funkts. Anal. Prilozh. 15, No.3, 1-9 (Russian) (1981; Zbl 0477.73052). Cited in 2 Documents MSC: 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) 74K15 Membranes 74K25 Shells 74H45 Vibrations in dynamical problems in solid mechanics 47Gxx Integral, integro-differential, and pseudodifferential operators 76D05 Navier-Stokes equations for incompressible viscous fluids 47A10 Spectrum, resolvent 47B38 Linear operators on function spaces (general) Keywords:distribution of frequencies; free vibrations of shells; filled with; nonviscous compressible liquid; system of coupled partial; differential equations; selfadjoint; asymptotic limits; bounds PDF BibTeX XML Cite \textit{A. G. Aslanyan} et al., Funct. Anal. Appl. 15, 157--163 (1982; Zbl 0576.73039) Full Text: DOI References: [1] V. N. Buivol, Oscillations and Stability of Deformable Systems in a Liquid [in Russian], Naukova Dumka, Kiev (1975). [2] L. I. Balabukh, ”Interaction of shells with liquid and gas,” in: Proceedings of the Sixth All-Union Conference on the Theory of Shells and Membranes [in Russian], Nauka, Moscow (1966). · Zbl 0153.11601 [3] A. L. Gol’denveizer, V. B. Lidskii, and P. E. Tovstik, Free Vibrations of Thin Elastic Shells [in Russian], Nauka, Moscow (1979). [4] A. G. Aslanyan and V. B. Lidskii, Distribution of the Natural Frequencies of Thin Elastic Shells [in Russian], Nauka, Moscow (1974). [5] J. L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, Springer-Verlag (1972). [6] I. M. Glazman, Direct Methods of the Qualitative Spectral Analysis of Singular Differential Operators [in Russian], Fizmatgiz, Moscow (1963). · Zbl 0143.36505 [7] D. G. Vasil’ev, ”Asymptotic of the distribution function of the spectra of pseudodifferential operators with parameters,” Funkts. Anal. Prilozhen.,14, No. 3, 65-66 (1980). [8] L. H?rmander, ”The spectral function of an elliptic operator,” Acta Math.,121, Nos. 3-4, 193-218 (1968). · Zbl 0164.13201 · doi:10.1007/BF02391913 [9] M. A. Shubin, Pseudodifferential Operators and Spectral Theory [in Russian], Nauka, Moscow (1978). · Zbl 0451.47064 [10] A. G. Aslanyan, D. G. Vasil’ev, and V. B. Lidskii, ”The frequencies of free vibrations of shells interacting with liquid,” in: Proceedings of the Twelfth All-Union Conference on the Theory of Shells and Membranes [in Russian], Erevan State Univ. (1980), pp. 86-92. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.