Abstract
We study the existence and uniqueness of the solution to the second initial boundary value problem for the gravitation-gyroscopic wave equation in an exterior multiply connected domain with various types of conditions at infinity.
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S. A. Gabov and P. V. Shevtsov, “Main boundary value problems for equations of oscillations of a stratified fluid,”Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],268, No. 6, 1293–1296 (1983).
S. A. Gabov and P. V. Shevtsov, “A differential equation of the type of the Sobolev equation,”Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],276, No. 1, 14–17 (1984).
P. V. Shevtsov,Main Initial Boundary Value Problems for an Equation of Composite Type [in Russian], Dep. VINITI No. 3882-83, Moscow (1983).
S. V. Uspenskii, G. V. Demidenko, and V. G. Perepelkin,Embedding Theorems and Applications to Differential Equations [in Russian], Nauka, Novosibirsk (1984).
S. A. Gabov and A. G. Sveshnikov,Linear Problems of the Theory of Nonstationary Interior Waves [in Russian], Nauka, Moscow (1980).
B. V. Kapitonov, “Theory of Potential for the Equation of Small Oscillations of a Rotating Fluid,”Mat. Sb. [Math. USSR-Sb.],109, No. 4, 607–628 (1979).
P.A.Krutitskii, “Explicit solution of the Dirichlet problem for an equation of composite type in a multiply connected domain,”Dokl. Ross. Akad. Nauk [Russian Math. Dokl.],325, No. 3, 428–433 (1992).
P.A.Krutitskii, “An initial boundary value problem describing oscillations of the system of plates in a stratified rotating fluid,” in:Calculus and Differential Equations [in Russian], Izd. Novosib. Univ., Novosibirsk (1991), pp. 78–88.
P. A. Krutitskii, in:Conf. on Evolution Equations, 25–29 July 1994. Abstracts of lectures, Strathclyde Univ, Glasgow (1994), p. 10.
A. M. Brekhovskikh and V. V. Goncharov,Introduction to Continuum Mechanics [in Russian], Nauka, Moscow (1982).
P. H. Le Blond and L. A. Mysak,Waves in the Ocean, Elsevier, Amsterdam (1978).
P. A. Krutitskii, “Initial and boundary value problems for the equation of a stratified rotating fluid,” in:Algebra and Calculus [in Russian], Izd. Novosib. Univ., Novosibirsk (1990), pp. 40–50.
V. S. Vladimirov,Equations of Mathematical Physics [in Russian], Nauka, Moscow (1981).
S. L. Sobolev,Selected Topics from the Theory of Function Spaces and Distributions [in Russian], Nauka, Moscow (1989).
N. I. Muskhelishvili,Singular Integral Equations [in Russian], Nauka, Moscow (1968).
P. A. Krutitskii, “The Dirichlet problem for the Helmholtz equation outside cuts on the plane,”Zh. Vychisl. Mat. i Mat. Fiz. [U.S.S.R. Comput. Math. and Math. Phys.],34, No. 8, 9, 1237–1258 (1994).
L. V. Kantorovich and G. P. Akilov,Functional Analysis [in Russian], Nauka, Moscow (1984).
S. G. Krein,Functional Analysis [in Russian], Nauka, Moscow (1964).
A. N. Kolmogorov and S. V. Fomin,Elements of Function Theory and Functional Analysis [in Russian], Nauka, Moscow (1972).
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Translated fromMatematicheskie Zametki, Vol. 60, No. 1, pp. 40–57, July, 1996.
This research was partially supported by the Russian Foundation for Basic Research under grant No. 96-01-01411.
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Krutitskii, P.A. The second initial boundary value problem for the gravitation-gyroscopic wave equation in exterior domains. Math Notes 60, 29–41 (1996). https://doi.org/10.1007/BF02308877
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DOI: https://doi.org/10.1007/BF02308877