Literature Cited
S. L. Sobolev, “On the motion of a symmetric top with a cavity filled with liquid,” Zh. Prikl. Mekh. Tekh. Fiz., No. 3, 20–55 (1960).
S. L. Sobolev, “On a new problem of mathematical physics,” Izv. Akad. Nauk SSSR, Ser. Mat.,18, No. 1, 3–50 (1954).
R. A. Aleksandryan, Yu. M. Berezanskii, V. A. Il'in, and A. G. Kostyuchenko, “Certain problems of the spectral theory for partial differential equations,” in: Partial Differential Equations [in Russian], Nauka, Moscow (1970), pp. 3–35.
A. A. Dezin and V. N. Maslennikova, “Nonclassical boundary-value problems,” ibid., 81–95.
T. I. Zelenyak and V. P. Mikhailov, “Asymptotic behavior of solutions of some boundary-value problems in mathematical physics as t→∞,” ibid., 96–118.
V. N. Maslennikova, “A mathematical study of rotating liquid hydrodynamics,” in: The National Conference on Partial Differential Equations [in Russian], Moscow State Univ. (1977), pp. 153–156.
A. A. Dezin, T. I. Zelenyak, and V. N. Maslennikova, “On certain mathematical problems in hydrodynamics,” in: Partial Differential Equations [in Russian], Nauka, Novosibirsk (1980), pp. 21–31.
G. V. Demidenko, V. G. Perepelkin, S. V. Uspenskii, and S. I. Yanov, “Boundary-value problems for equations and systems of Sobolev type,” in: Partial Differential Equations [in Russian], Nauka, Novosibirsk (1986), pp. 72–84.
G. I. Marchuk, Numerical Solution of the Problems of Atmosphere and Ocean Dynamics [in Russian], Gidrometeoizdat, Leningrad (1974).
V. V. Penenko and A. E. Aloyan, Models and Methods for Solving Environment Protection Problems [in Russian], Nauka, Novosibirsk (1985).
L. M. Brekhovskikh and V. V. Goncharov, Introduction to Mechanics of Continua [in Russian], Nauka, Moscow (1982).
V. N. Maslennikova and Pal Prodip Kumar, “On stabilization and limit amplitude of a solution to the Cauchy problem for nonhomogeneous Sobolev systems,” Sib. Mat. Zh.,27, No. 3, 142–153 (1986).
F. Riesz and B. Szokefalvi-Nagy, Lectures in Functional Analysis [Russian translation], Mir, Moscow (1979).
T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, New York (1966).
M. E. Bogovskii, “Decomposition ofL 2(Ω;R n) into the direct sum of the subspaces of solenoidal and potential vector fields,” Sov. Math. Dokl.,33, No. 1, 161–165 (1986).
J. V. Ralston, “On stationary modes in inviscid rotating fluids,” J. Math. Anal. Appl.,44, 366–383 (1973).
S. L. Sobolev, Applications of Functional Analysis in Mathematical Physics [in Russian], Nauka, Novosibirsk (1962).
P. K. Pal and V. N. Maslennikova, “Spectral properties of operators in the problem of the oscillation of a compressible fluid in rotating containers,” Sov. Math. Dokl.,31, No. 2, 318–322 (1985).
S. Agmon, A. Douglis, and L. Nirenberg, “Estimates near the boundary for solutions of elliptic differential equations,” Commun. Pure Appl. Math.,17, 35–92 (1964).
G. Grubb and G. Geymonat, “The essential spectrum of elliptic systems of mixed order,” Math. Ann.,227, 257–276 (1977).
G. Talenti, “Spectrum of the Laplace operator acting inL p (R n),” Symposia Mathematica Instituto Nazionale di Alta Mathematica,7 (1971).
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Dedicated to the 80th birthday of Sergei L'vovich Sobolev.
Moscow. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 29, No. 5, pp. 157–171, September–October, 1988.
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Maslennikova, V.N., Giniatullin, A.I. Spectral properties of operators for the systems of hydrodynamics of a rotating liquid and nonuniqueness of the limit amplitude. Sib Math J 29, 812–824 (1988). https://doi.org/10.1007/BF00970278
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DOI: https://doi.org/10.1007/BF00970278