| Title:
|
Functionals on function and sequence spaces connected with the exponential stability of evolutionary processes (English) |
| Author:
|
Preda, Petre |
| Author:
|
Pogan, Alin |
| Author:
|
Preda, Ciprian |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
2 |
| Year:
|
2006 |
| Pages:
|
425-435 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
evolutionary processes |
| Keyword:
|
uniform exponential stability |
| MSC:
|
34D05 |
| MSC:
|
34D20 |
| MSC:
|
34G10 |
| MSC:
|
46B45 |
| MSC:
|
47D06 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 1164.34432 |
| idMR:
|
MR2291747 |
| . |
| Date available:
|
2009-09-24T11:34:23Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128077 |
| . |
| Reference:
|
[1] R. Datko: Extending a theorem of Liapunov to Hilbert spaces.J. Math. Anal. Appl. 32 (1970), 610–616. MR 0268717, 10.1016/0022-247X(70)90283-0 |
| Reference:
|
[2] R. Datko: Uniform asymptotic stability of evolutionary processes in a Banach space.SIAM. J. Math. Analysis 3 (1973), 428–445. MR 0320465 |
| Reference:
|
[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 |
| Reference:
|
[4] W. Littman: A generalization of the theorem Datko-Pazy.Lecture Notes in Control and Inform. Sci., Springer Verlag 130 (1989), 318–323. MR 1029070, 10.1007/BFb0043280 |
| Reference:
|
[5] J. M. A. M. van Neerven: Exponential stability of operators and semigroups.J. Func. Anal. 130 (1995), 293–309. MR 1335382, 10.1006/jfan.1995.1071 |
| Reference:
|
[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 |
| Reference:
|
[7] J. M. A. M. van Neerven: Lower semicontinuity and the theorem of Datko and Pazy.Int. Eq. Op. Theory 42 (2002), 482–492. Zbl 1040.47033, MR 1885446, 10.1007/BF01270925 |
| Reference:
|
[8] A. Pazy: On the applicability of Liapunov’s theorem in Hilbert spaces.SIAM. J. Math. Anal. Appl. 3 (1972), 291–294. MR 0317105, 10.1137/0503028 |
| Reference:
|
[9] A. Pazy: Semigroups of Linear Operators and Applications to Partial Differential Equations.Springer-Verlag, 1983. Zbl 0516.47023, MR 0710486 |
| Reference:
|
[10] S. Rolewicz: On uniform N-equistability.J. Math. Anal. Appl. 115 (1986), 434–441. Zbl 0597.34064, MR 0836237 |
| Reference:
|
[11] J. Zabczyk: Remarks on the control of discrete-time distributed parameter systems.SIAM J. Control. Optim. 12 (1974), 721–735. Zbl 0254.93027, MR 0410506, 10.1137/0312056 |
| . |
