SpringerLink
Log in

Analysis of spectral properties of operators for linearized steady-state equations of a viscous compressible heat-conducting fluid

  • Published:
Journal of Dynamical and Control Systems Aims and scope Submit manuscript

Abstract

The spectrum of operators for linearized steady-state equations of a viscous, compressible, heat-conducting fluid is studied. Using the factorization of operators and applying the theory of pseudo-differential operators, we prove that the operator is sectorial and its spectrum is discrete everywhere except for some segment on the real line. This segment is the essential spectrum of the operator and it lies in the left half-plane.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. S. Agranovich, Elliptic operators on closed manifolds. Itogi Nauki Tekhn. 63 (1990), 5–129.

    MathSciNet  MATH  Google Scholar 

  2. M. S. Agranovich and M. I. Vishik, Elliptic problems with a parameter and parabolic problems of general type. Usp. Mat. Nauk 19 (1964), No. 3, 53–161.

    MATH  Google Scholar 

  3. F. V. Atkinson, H. Langer, R. Mennicken, and A. A. Shkalikov, The essential spectrum of some matrix operators. Math. Nachr. 167 (1994), 5–20.

    Article  MathSciNet  MATH  Google Scholar 

  4. A. V. Fursikov, Stabilizability of quasilinear parabolic equation by feedback boundary control. Mat. Sb. 192 (2001), No. 4, 593–639.

    Article  MathSciNet  MATH  Google Scholar 

  5. _____, Stabilization from the boundary of solutions to the Navier–Stokes system: Solvability and justification of the numerical simulation. Dalnevost. Mat. Zh. 4 (2003), No. 1, 86–100.

  6. I. Ts. Gohberg and M. G. Krein, Introduction to the theory of linear nonselfadjoint operators. AMS (1969).

  7. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics. Vol. 6. Fluid Mechanics. Butterworth-Heinemann (1987).

    Google Scholar 

  8. M. R. Levitin, Vibrations of a viscous compressible fluid in bounded domains: spectral properties and asymptotics. Asympt. Anal. 7 (1993), 15–34.

    MathSciNet  MATH  Google Scholar 

  9. _____, Vibrations of a viscous compressible fluid in bounded and unbounded domains. Math. Meth. Fluid Mech. 274 (1991), 251–255.

  10. M. Nunez, Spectral analysis of viscous static compressible fluid equilibria. J. Phys. A: Math. Gen. 34 (2001), 4341–4352.

    Article  MathSciNet  MATH  Google Scholar 

  11. M. A. Pribyl, Spectral analysis of linearized stationary equations of a compressible viscous fluid. Mat. Sb. 198 (2007), No. 10, 119–140.

    MathSciNet  Google Scholar 

  12. _____, Spectral analysis of linearized stationary equations of a viscous compressible fluid in ℝ3 with periodic boundary conditions. Algebra Anal. 20 (2008), No. 2, 149–177.

Download references

Author information

Authors and Affiliations

  1. Scientific Research Institute of System Development, Moscow, Russia

    M. Pribyl

Authors
  1. M. Pribyl
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Pribyl.

Additional information

This work was partially supported by the Russian Foundation for Basic Research (project No. 10-01-00136).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pribyl, M. Analysis of spectral properties of operators for linearized steady-state equations of a viscous compressible heat-conducting fluid. J Dyn Control Syst 17, 187–205 (2011). https://doi.org/10.1007/s10883-011-9115-2

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10883-011-9115-2

Key words and phrases

2000 Mathematics Subject Classification

Search

Navigation