On Properties of Root Elements in the
Problem on Small Motions of Viscous
Relaxing Fluid
D. Zakora

Voronezh State University
1 University Sq., Voronezh, 394006, Russia
E-mail: dmitry_@crimea.edu, dmitry.zkr@gmail.com

Received October 20, 2015, revised May 11, 2016

Abstract

In the present work, the properties of root elements of the problem on
small motions of a viscous relaxing
fluid completely filling a bounded domain
are studied. A multiple p -basis property of special system of elements is
proven for the case where the system is in weightlessness. The solution of
the evolution problem is expanded with respect to the corresponding system.

Mathematics Subject Classification 2000: 45K05, 58C40, 76R99.Key words: viscous fluid, compressible fluid, basis.

References
[1] D. Zakora, On the Spectrum of Rotating Viscous Relaxing Fluid, Zh. Mat. Fiz.Anal. Geom. 12 (2016), No. 4, 338–358.

[2] D. Zakora, A Symmetric Model of Viscous Relaxing Fluid. An Evolution Problem,Zh. Mat. Fiz. Anal. Geom. 8 (2012), No. 2, 190–206.

[3] A.S. Marcus, Introduction to Spectral Theory of Polinomial Operator Pencils, Shti-inca, Kishenev, 1986 (Russian).

[4] D.A. Zakora, Operator Approach to Ilushin’s Model of Viscoelastic Body ofParabolic Type, Sovrem. Mat. Fundam. Napravl. 57 (2015), 31–64 (Russian); Engl.transl.: J. Math. Sci. (N.Y.) 225 (2015), No. 2, 345–380.

[5]T.Ya. Azizov and I.S. Iohvidov, Basic Operator Theory in Spaces with IndeﬁniteMetrics, Nauka, Moscow, 1986 (Russian).

[6] N.D. Kopachevsky and S.G. Krein, Operator Approach to Linear Problems of Hy-drodynamics. Vol. 2: Nonself-Adjoint Problems for Viscous Fluids, Birkh¨auser Ver-lag, Basel–Boston–Berlin, 2003.