The linearized uniform asymptotic stability of evolution differential equations

Jiří Neustupa

Czechoslovak Mathematical Journal (1984)

  • Volume: 34, Issue: 2, page 257-284
  • ISSN: 0011-4642

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Neustupa, Jiří. "The linearized uniform asymptotic stability of evolution differential equations." Czechoslovak Mathematical Journal 34.2 (1984): 257-284. <http://eudml.org/doc/13449>.

@article{Neustupa1984,
author = {Neustupa, Jiří},
journal = {Czechoslovak Mathematical Journal},
keywords = {method of linearization; uniform asymptotic stability; Navier-Stokes equations; wave equation; equation of oscillations of a beam; Timoshenko- type equation},
language = {eng},
number = {2},
pages = {257-284},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The linearized uniform asymptotic stability of evolution differential equations},
url = {http://eudml.org/doc/13449},
volume = {34},
year = {1984},
}

TY - JOUR
AU - Neustupa, Jiří
TI - The linearized uniform asymptotic stability of evolution differential equations
JO - Czechoslovak Mathematical Journal
PY - 1984
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 34
IS - 2
SP - 257
EP - 284
LA - eng
KW - method of linearization; uniform asymptotic stability; Navier-Stokes equations; wave equation; equation of oscillations of a beam; Timoshenko- type equation
UR - http://eudml.org/doc/13449
ER -

References

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  1. Barták J., Lyapunov Stability and Stability at Constantly Acting Disturbances of an Abstract Differential Equation of the Second Order, Czech. Math. Journal 26, 411 - 437, 1976. (1976) MR0415017
  2. Barták J., Stability and Correctness of Abstract Differential Equations in Hilbert Spaces, Czech. Math. Journal 28, 548-593, 1978. (1978) MR0499545
  3. Barták J. J. Neustupa, A Note to Stability of the Equation of Oscillations of a Beam, (Russian). Čas. pro pěst. mat. 104, 338-352, 1979. (1979) MR0553168
  4. Daleckij J. L. M. G. Krejn, Stability of Solutions of Diflferential Equations in Banach Space, Moscow, Nauka 1970. (Russian) (1970) MR0352638
  5. Dunford N.. J. T. Schwartz, Linear Operators I, New York, John Wiley & Sons, Inc. 1958. (1958) 
  6. Hahn W., Stability of Motion, Berlin-Heidelberg-New York, Springer-Verlag 1967. (1967) Zbl0189.38503MR0223668
  7. Iooss G., 10.1007/BF00281481, Arch Rat. Mech. Anal. 40, 166-208, 1971. (1971) Zbl0218.76059MR0269178DOI10.1007/BF00281481
  8. Iooss G., 10.1007/BF00281637, Arch. Rat. Mech. Anal. 47, 301-329, 1972. (1972) Zbl0258.35057MR0346350DOI10.1007/BF00281637
  9. Iooss G., 10.1007/BF00280153, Arch. Rat. Mech. Anal. 58, 35-56, 1975. (1975) Zbl0337.35058MR0393885DOI10.1007/BF00280153
  10. Kato T., Perturbation Theory for Linear Operators, Berlin-Heidelberg-New York, Springer-Verlag 1976. (1976) Zbl0342.47009MR0407617
  11. Kielhöfer H., 10.1007/BF00248417, Arch. Rat. Mech. Anal. 57, 150-165, 1974. (1974) MR0442405DOI10.1007/BF00248417
  12. Kielhöfer H., 10.1016/0022-0396(76)90011-5, Journal of Diff. Equations 22, 193-208, 1976. (1976) MR0450762DOI10.1016/0022-0396(76)90011-5
  13. Ladyzhenskaya O. A., The Mathematical Theory of Viscous Incompressible Flow, Moscow, Nauka 1970. (Russian) (1970) MR0254401
  14. Ladyzhenskaya O. A. V. A. Solonnikov, On the Principle of Linearization and Invariant Manifolds for Problems of Magnetohydrodynamics, Zapisky naučnych seminarov LOMI, Vol. 38, Boundary-Value Problems of Math. Physics and Related Questions of the Function Theory 7, 46-93, Nauka 1973. (Russian) (1973) MR0377310
  15. Neustupa J., The Uniform Exponential Stability and the Uniform Stability at Constantly Acting Disturbances of a Periodic Solution of the Wave Equation, Czech, Math. Journal 26, 388-410, 1976. (1976) MR0435565
  16. Neustupa J., A Contribution to the Theory of Stability of Differential Equations in Banach Space, Czech. Math. Journal 29, 27-52, 1979. (1979) Zbl0441.34044MR0518138
  17. Neustupa J., The Uniform Stability at Permanently Acting Disturbances of Evolution Differential Equations, To appear. MR1265180
  18. Prodi G., Teoremi di tipo locale per il sistema di Navier-Stokes e stabilita del le soluzioni stazionarie, Rend. Sem. Mat. Univ. Padova 32, 374-397, 1962. (1962) MR0189354
  19. Sattinger D. H., The Mathematical Problem of Hydrodynamic Stability, Journal of Math. and Mech. 18, 797-817, 1970. (1970) Zbl0198.30401MR0261182
  20. Sattinger D. H., Topics in Stability and Bifurcation Theory, Lecture Notes in Mathematics, n. 309, Berlin-Heidelberg-New York, Springer-Verlag 1973. (1973) Zbl0248.35003MR0463624
  21. Solonnikov V. A., Estimations of Solutions of the Nonstationary Navier-Stokes System, Zapisky naucnych seminarov LOMI, Vol. 38, Boundary-Value Problems of Math. Physics and Related Questions of the Function Theory 7, 153 - 231, Nauka 1973. (Russian) (1973) MR0415097
  22. Sova M., Linear Differential Equations in Banach Spaces, Rozpravy ČSAV, Series of Math. and Natural Sciences, Vol. 85, No. 6, Academia Praha, 1975. (1975) Zbl0333.34055MR0481342
  23. Strauss A. J. A. Yorke, 10.1016/0022-0396(69)90004-7, Journal of Diff. Equations 6, 452-483, 1969. (1969) MR0252781DOI10.1016/0022-0396(69)90004-7
  24. Travis С. С. G. F. Webb, 10.1090/S0002-9947-1974-0382808-3, Transactions of the Amer. Math. Soc. 200, 395-418, 1974. (1974) MR0382808DOI10.1090/S0002-9947-1974-0382808-3
  25. Yosida K., Functional Analysis, Berlin-Heidelberg-New York, Springer-Verlag 1971. (1971) Zbl0217.16001

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