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Article

Preda, Petre ; Pogan, Alin ; Preda, Ciprian
Functionals on function and sequence spaces connected with the exponential stability of evolutionary processes. (English). Czechoslovak Mathematical Journal, vol. 56 (2006), issue 2, pp. 425-435
MSC: 34D05, 34D20, 34G10, 46B45, 47D06, 47N20 | MR 2291747 | Zbl 1164.34432
Keywords:
evolutionary processes; uniform exponential stability
Summary:
The exponential stability property of an evolutionary process is characterized in terms of the existence of some functionals on certain function spaces. Thus are generalized some well-known results obtained by Datko, Rolewicz, Littman and Van Neerven.
References:
[1] R. Datko: Extending a theorem of Liapunov to Hilbert spaces. J. Math. Anal. Appl. 32 (1970), 610–616. DOI 10.1016/0022-247X(70)90283-0 | MR 0268717
[2] R. Datko: Uniform asymptotic stability of evolutionary processes in a Banach space. SIAM. J. Math. Analysis 3 (1973), 428–445. MR 0320465
[3] E. Hille and R. S. Phillips: Functional Analysis and Semi-groups (revised edition). Amer. Math. Soc. Colloq. Publ. Vol. 31, Providence, R.I., 1957. MR 0089373
[4] W. Littman: A generalization of the theorem Datko-Pazy. Lecture Notes in Control and Inform. Sci., Springer Verlag 130 (1989), 318–323. DOI 10.1007/BFb0043280 | MR 1029070
[5] J. M. A. M. van Neerven: Exponential stability of operators and semigroups. J. Func. Anal. 130 (1995), 293–309. DOI 10.1006/jfan.1995.1071 | MR 1335382
[6] J. M. A. M. van Neerven: The Asymptotic Behaviour of Semigroups of Linear Operators, Theory, Advances and Applications, Vol. 88. Birkhauser, 1996. MR 1409370
[7] J. M. A. M. van Neerven: Lower semicontinuity and the theorem of Datko and Pazy. Int. Eq. Op. Theory 42 (2002), 482–492. DOI 10.1007/BF01270925 | MR 1885446 | Zbl 1040.47033
[8] A. Pazy: On the applicability of Liapunov’s theorem in Hilbert spaces. SIAM. J. Math. Anal. Appl. 3 (1972), 291–294. DOI 10.1137/0503028 | MR 0317105
[9] A. Pazy: Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, 1983. MR 0710486 | Zbl 0516.47023
[10] S. Rolewicz: On uniform N-equistability. J. Math. Anal. Appl. 115 (1986), 434–441. MR 0836237 | Zbl 0597.34064
[11] J. Zabczyk: Remarks on the control of discrete-time distributed parameter systems. SIAM J. Control. Optim. 12 (1974), 721–735. DOI 10.1137/0312056 | MR 0410506 | Zbl 0254.93027
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