Geodesic
Spectral properties of operators in the problem on normal oscillations of~a~mixture of viscous compressible fluids
Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 1, pp. 73-97

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In this paper, we study a problem of normal oscillations of a homogeneous mixture of several viscous compressible fluids filling a bounded domain of three-dimensional space with an infinitely smooth boundary. Two boundary conditions are considered: the no-slip condition and the slip condition without shear stresses. It is proved that the essential spectrum of the problem in both cases is a finite set of segments located on the real axis. The discrete spectrum lies on the real axis, except perhaps for a finite number of complex conjugate eigenvalues. The spectrum of the problem contains a subsequence of eigenvalues with a limit point at infinity and a power-law asymptotic distribution.
Keywords: mixture of fluids, spectral problem, essential spectrum, discrete spectrum.
Mots-clés : compressible viscous fluid 
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D. A. Zakora. Spectral properties of operators in the problem on normal oscillations of~a~mixture of viscous compressible fluids. Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 1, pp. 73-97. http://geodesic.mathdoc.fr/item/CMFD_2023_69_1_a5/