Exponential dichotomy of evolution equations and admissibility of function spaces on a half-line

Journal of Functional Analysis

Volumn 235, Issue 1, 2006, Pages 330-354

  Huy, Nguyen Thieu ^a  

^a HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Viet Nam)

Author keywords

Admissibility of function spaces; Evolution equations; Exponential dichotomy; Exponential stability of solutions; Integral equations; Perturbations

Indexed keywords

EID: 33749572614     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2005.11.002     Document Type: Article

References (29)

1. Ben-Artzi A., and Gohberg I. Dichotomies of systems and invertibility of linear ordinary differential operators. Oper. Theory Adv. Appl. 56 (1992) 90-119
2. Ben-Artzi A., Gohberg I., and Kaashoek M.A. Invertibility and dichotomy of differential operators on a half-line. J. Dynam. Differential Equations 5 (1993) 1-36
3. Brendle S., and Nagel R. Partial functional equations with non-autonomous past. Discrete Contin. Dyn. Syst. 8 (2002) 953-966
4. ∞ and the theorem of Marcinkiewicz. Studia Math. 26 (1996) 273-299
5. Coppel W.A. Dichotomy in Stability Theory (1978), Springer-Verlag, Berlin
6. Daleckii J.L., and Krein M.G. Stability of Solutions of Differential Equations in Banach Spaces. Transl. Amer. Math. Soc. (1974), Amer. Math. Soc., Providence, RI
7. Datko R. Uniform asymptotic stability of evolutionary processes in a Banach space. SIAM J. Math. Anal. 3 (1972) 428-445
8. Engel K.J., and Nagel R. One-Parameter Semigroups for Linear Evolution Equations. Grad. Texts in Math. vol. 194 (2000), Springer-Verlag, Berlin
9. Huy N.T., and Minh N.V. Exponential dichotomy of difference equations and applications to evolution equations on the half-line. Comput. Math. Appl. 42 (2001) 301-311
10. Huy N.T. Resolvents of operators and partial functional differential equations with non-autonomous past. J. Math. Anal. Appl. 289 (2004) 301-316
11. Huy N.T. Exponentially dichotomous operators and exponential dichotomy of evolution equations on the half-line. Integral Equations Operator Theory 48 (2004) 497-510
12. Kato T. Perturbation Theory for Linear Operators (1980), Springer-Verlag, Berlin
13. Levitan B.M., and Zhikov V.V. Almost Periodic Functions and Differential Equations (1978), Moscow Univ. Publ. House English translation:
14. Levitan B.M., and Zhikov V.V. Almost Periodic Functions and Differential Equations (1982), Cambridge Univ. Press, Cambridge
15. Lindenstrauss J., and Tzafriri L. Classical Banach Spaces II, Function Spaces (1979), Springer-Verlag, Berlin
16. Massera J.J., and Schäffer J.J. Linear Differential Equations and Function Spaces (1966), Academic Press, New York
17. Minh N.V., and Huy N.T. Characterizations of dichotomies of evolution equations on the half-line. J. Math. Anal. Appl. 261 (2001) 28-44
18. Minh N.V., Räbiger F., and Schnaubelt R. Exponential dichotomy exponential expansiveness and exponential dichotomy of evolution equations on the half-line. Integral Equations Operator Theory 32 (1998) 332-353
19. Nagel R., and Nickel G. Well-posedness for non-autonomous abstract Cauchy problems. Progr. Nonlinear Differential Equations Appl. vol. 50 (2002), Birkhäuser, Boston, MA 279-293
20. van Neerven J. The Asymptotic Behaviour of Semigroups of Linear Operator. Oper. Theory Adv. Appl. vol. 88 (1996), Birkhäuser, Basel
21. G. Nickel, On evolution semigroups and wellposedness of non-autonomous Cauchy problems, PhD thesis, Tübingen, 1996
22. Pazy A. Semigroup of Linear Operators and Application to Partial Differential Equations (1983), Springer-Verlag, Berlin
23. Perron O. Die Stabilitätsfrage bei Differentialgleichungen. Math. Z. 32 (1930) 703-728
24. Räbiger F., and Schnaubelt R. Absorption evolution families with applications to non-autonomous diffusion processes. Tübinger Ber. Funktionalanalysis 5 (1995/1996) 335-354
25. Räbiger F., and Schnaubelt R. The spectral mapping theorem for evolution semigroups on spaces of vector-valued functions. Semigroup Forum 48 (1996) 225-239
26. R. Schnaubelt, Exponential bounds and hyperbolicity of evolution families, PhD thesis, Tübingen, 1996
27. Schnaubelt R. Exponential dichotomy of non-autonomous evolution equations (1999), Habilitationsschrift, Tübingen
28. Schnaubelt R. Asymptotically autonomous parabolic evolution equations. J. Evol. Equ. 1 (2001) 19-37
29. Triebel H. Interpolation Theory, Function Spaces, Differential Operators (1978), North-Holland, Amsterdam