| Title:
|
The linearized uniform asymptotic stability of evolution differential equations (English) |
| Author:
|
Neustupa, Jiří |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
34 |
| Issue:
|
2 |
| Year:
|
1984 |
| Pages:
|
257-284 |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| MSC:
|
34G20 |
| MSC:
|
35B35 |
| idZBL:
|
Zbl 0599.34081 |
| idMR:
|
MR743491 |
| DOI:
|
10.21136/CMJ.1984.101949 |
| . |
| Date available:
|
2008-06-09T14:59:48Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/101949 |
| . |
| Reference:
|
[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. MR 0415017 |
| Reference:
|
[2] Barták J.: Stability and Correctness of Abstract Differential Equations in Hilbert Spaces.Czech. Math. Journal 28, 548-593, 1978. MR 0499545 |
| Reference:
|
[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. MR 0553168 |
| Reference:
|
[4] Daleckij J. L. M. G. Krejn: Stability of Solutions of Diflferential Equations in Banach Space.Moscow, Nauka 1970. (Russian) MR 0352638 |
| Reference:
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[5] Dunford N.. J. T. Schwartz: Linear Operators I.New York, John Wiley & Sons, Inc. 1958. |
| Reference:
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[6] Hahn W.: Stability of Motion.Berlin-Heidelberg-New York, Springer-Verlag 1967. Zbl 0189.38503, MR 0223668 |
| Reference:
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[7] Iooss G.: Theorie non linéaire de la stabilité des écoulements laminaires dans le cas de "l'échange des stabilités".Arch Rat. Mech. Anal. 40, 166-208, 1971. Zbl 0218.76059, MR 0269178, 10.1007/BF00281481 |
| Reference:
|
[8] Iooss G.: Existence et stabilité de la solution périodique secondaire intervenant dans les problèmes d'évolution du type Navier-Stokes.Arch. Rat. Mech. Anal. 47, 301-329, 1972. Zbl 0258.35057, MR 0346350, 10.1007/BF00281637 |
| Reference:
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[9] Iooss G.: Bifurcation of a Periodic Solution of the Navier-Stokes Equations into an Invariant Torus.Arch. Rat. Mech. Anal. 58, 35-56, 1975. Zbl 0337.35058, MR 0393885, 10.1007/BF00280153 |
| Reference:
|
[10] Kato T.: Perturbation Theory for Linear Operators.Berlin-Heidelberg-New York, Springer-Verlag 1976. Zbl 0342.47009, MR 0407617 |
| Reference:
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[11] Kielhöfer H.: Stability and Semilinear Evolution Equations in Hubert Space.Arch. Rat. Mech. Anal. 57, 150-165, 1974. MR 0442405, 10.1007/BF00248417 |
| Reference:
|
[12] Kielhöfer H.: On the Lyapunov Stability of Stationary Solutions of Semilinear Parabolic Differential Equations.Journal of Diff. Equations 22, 193-208, 1976. MR 0450762, 10.1016/0022-0396(76)90011-5 |
| Reference:
|
[13] Ladyzhenskaya O. A.: The Mathematical Theory of Viscous Incompressible Flow.Moscow, Nauka 1970. (Russian) MR 0254401 |
| Reference:
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[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) MR 0377310 |
| Reference:
|
[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. MR 0435565 |
| Reference:
|
[16] Neustupa J.: A Contribution to the Theory of Stability of Differential Equations in Banach Space.Czech. Math. Journal 29, 27-52, 1979. Zbl 0441.34044, MR 0518138 |
| Reference:
|
[17] Neustupa J.: The Uniform Stability at Permanently Acting Disturbances of Evolution Differential Equations.To appear. MR 1265180 |
| Reference:
|
[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. MR 0189354 |
| Reference:
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[19] Sattinger D. H.: The Mathematical Problem of Hydrodynamic Stability.Journal of Math. and Mech. 18, 797-817, 1970. Zbl 0198.30401, MR 0261182 |
| Reference:
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[20] Sattinger D. H.: Topics in Stability and Bifurcation Theory.Lecture Notes in Mathematics, n. 309, Berlin-Heidelberg-New York, Springer-Verlag 1973. Zbl 0248.35003, MR 0463624 |
| Reference:
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[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) MR 0415097 |
| Reference:
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[22] Sova M.: Linear Differential Equations in Banach Spaces.Rozpravy ČSAV, Series of Math. and Natural Sciences, Vol. 85, No. 6, Academia Praha, 1975. Zbl 0333.34055, MR 0481342 |
| Reference:
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[23] Strauss A. J. A. Yorke: Perturbing Uniformly Asymptotically Stable Nonlinear Systems.Journal of Diff. Equations 6, 452-483, 1969. MR 0252781, 10.1016/0022-0396(69)90004-7 |
| Reference:
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[24] Travis С. С. G. F. Webb: Existence and Stability for Partial Differential Equations.Transactions of the Amer. Math. Soc. 200, 395-418, 1974. MR 0382808, 10.1090/S0002-9947-1974-0382808-3 |
| Reference:
|
[25] Yosida K.: Functional Analysis.Berlin-Heidelberg-New York, Springer-Verlag 1971. Zbl 0217.16001 |
| . |
