# Exponential expansiveness and complete admissibility for evolution families

Mihail Megan; Bogdan Sasu; Adina Luminiţa Sasu

Czechoslovak Mathematical Journal (2004)

- Volume: 54, Issue: 3, page 739-749
- ISSN: 0011-4642

## Access Full Article

top## Abstract

top## How to cite

topMegan, Mihail, Sasu, Bogdan, and Sasu, Adina Luminiţa. "Exponential expansiveness and complete admissibility for evolution families." Czechoslovak Mathematical Journal 54.3 (2004): 739-749. <http://eudml.org/doc/30896>.

@article{Megan2004,

abstract = {Connections between uniform exponential expansiveness and complete admissibility of the pair $(c_0(\{\mathbb \{N\}\}, X),c_0(\{\mathbb \{N\}\}, X))$ are studied. A discrete version for a theorem due to Van Minh, Räbiger and Schnaubelt is presented. Equivalent characterizations of Perron type for uniform exponential expansiveness of evolution families in terms of complete admissibility are given.},

author = {Megan, Mihail, Sasu, Bogdan, Sasu, Adina Luminiţa},

journal = {Czechoslovak Mathematical Journal},

keywords = {evolution family; uniform exponential expansiveness; complete admissibility; evolution family; uniform exponential expansiveness; complete admissibility},

language = {eng},

number = {3},

pages = {739-749},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Exponential expansiveness and complete admissibility for evolution families},

url = {http://eudml.org/doc/30896},

volume = {54},

year = {2004},

}

TY - JOUR

AU - Megan, Mihail

AU - Sasu, Bogdan

AU - Sasu, Adina Luminiţa

TI - Exponential expansiveness and complete admissibility for evolution families

JO - Czechoslovak Mathematical Journal

PY - 2004

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 54

IS - 3

SP - 739

EP - 749

AB - Connections between uniform exponential expansiveness and complete admissibility of the pair $(c_0({\mathbb {N}}, X),c_0({\mathbb {N}}, X))$ are studied. A discrete version for a theorem due to Van Minh, Räbiger and Schnaubelt is presented. Equivalent characterizations of Perron type for uniform exponential expansiveness of evolution families in terms of complete admissibility are given.

LA - eng

KW - evolution family; uniform exponential expansiveness; complete admissibility; evolution family; uniform exponential expansiveness; complete admissibility

UR - http://eudml.org/doc/30896

ER -

## References

top- 10.1007/BF01063733, J. Dynam. Differential Equations 5 (1993), 1–36. (1993) MR1205452DOI10.1007/BF01063733
- 10.1090/surv/070, Amer. Math. Soc., , 1999. (1999) MR1707332DOI10.1090/surv/070
- 10.1006/jdeq.1995.1117, J. Differential Equations 120 (1995), 429–477. (1995) MR1347351DOI10.1006/jdeq.1995.1117
- Stability of Solutions of Differential Equations in Banach Spaces. Trans. Math. Monographs 43, AMS, Providence, 1974. (1974) MR0352639
- Geometric Theory of Semilinear Parabolic Equations, Springer-Verlag, New York, 1981. (1981) Zbl0456.35001MR0610244
- 10.1007/BF01203919, Integral Equations Operator Theory 23 (1995), 472–500. (1995) MR1361056DOI10.1007/BF01203919
- 10.1006/jdeq.1999.3668, J. Differential Equations 159 (1999), 321–369. (1999) MR1730724DOI10.1006/jdeq.1999.3668
- On uniform exponential stability of periodic evolution operators in Banach spaces, Acta Math. Univ. Comenian. 69 (2000), 97–106. (2000) MR1796790
- On uniform exponential stability of linear skew-product semiflows in Banach spaces, Bull. Belg. Math. Soc. Simon Stevin 9 (2002), 143–154. (2002) MR1905653
- Discrete admissibility and exponential dichotomy for evolution families, Discrete Contin. Dynam. Systems 9 (2003), 383–397. (2003) MR1952381
- 10.1007/BF01197861, Integral Equations Operator Theory 44 (2002), 71–78. (2002) MR1913424DOI10.1007/BF01197861
- 10.1007/BF01203774, Integral Equations Operator Theory 32 (1998), 332–353. (1998) MR1652689DOI10.1007/BF01203774
- Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, Berlin-Heidelberg-New York, 1983. (1983) Zbl0516.47023MR0710486
- Robustness of exponential dichotomies in infinite-dimensional dynamical systems, J. Dynam. Differential Equations 3 (1999), 471–513. (1999) MR1693858

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.