PFDE with nonautonomous past

Discrete and Continuous Dynamical Systems

Volumn 8, Issue 4, 2002, Pages 953-966

  Brendle, Simon ^a   Nagel, Rainer ^a  

^a UNIVERSITY OF TÜBINGEN   (Germany)

Author keywords

Evolution semigroups; Nonautonomous Cauchy problem; pde with delay; Stability

Indexed keywords

EID: 0036787984     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2002.8.953     Document Type: Article

References (35)

1. M. Blake, A spectral bound for asymptotically norm continuous semigroups, J. Op. Th. 45 (2001), 111-130.
2. S. Brendle, R. Nagel and J. Poland, On the spectral mapping theorem for perturbed strongly continuous semigroups, Arch. Math. 74 (2000), 365-378.
3. C. Chicone and Y. Latushkin, Evolution Semigroups in Dynamical Systems and Differential Equations, Amer. Math. Soc., 1999.
4. O. Diekmann, M. Gyllenberg and H.R. Thieme, Perturbing evolutionary systems by step responses and cumulative outputs, J. Diff. Int. Eq. 8 (1995), 1205-1244.
5. O. Diekmann, S.A. van Gils, S.M. Verduyn Lunel and H.-O. Walther, Delay Equations, Springer-Verlag, 1995.
6. K.-J. Engel, Spectral theory and generator property of one-sided coupled operator matrices, Semigroup Forum 58 (1999), 267-295.
7. K.-J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Graduate Text in Math., Springer-Verlag, 2000.
8. J.K. Hale and S.M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer-Verlag, 1993.
9. G. Fragnelli, Classical solution for partial functional differential equations with nonautonomous past, to appear in Archiv Math.
10. M.I. Gil', Existence and stability of periodic solutions of semilinear neutral type systems, Discrete and Continuous Dynamical Systems 7 (2001), 809-820.
11. N.V.Minh, F. Räbiger and R. Schnaubelt, Exponential dichotomy exponential expansiveness and exponential dichotomy of evolution equation on the half line, Int. Eq. Op. Th. 32 (1998), 332-353.
12. N.V. Minh and N.T. Huy Characterizations of dichotomies of evolution equations on the half-line, J. Math. Anal. Appl. 261 (2001), 28-44.
13. R. Nagel (ed.), One-Parameter Semigroups of Positive Operators, Lect. Notes in Math., vol. 1184, Springer-Verlag, 1986.
14. R. Nagel, Characteristic equations for the spectrum of generators, Ann. Scuola Norm. Sup. Pisa 24 (1997), 703-717.
15. R. Nagel, Stability criteria through characteristic equations of linear operators, Rev. Unión Mat. Argentina 41 (1998), 91-98.
16. R. Nagel and S. Piazzera, On the regularity properties of perturbed semigroups, Rend. Circ. Mat. Palermo 58 (1998), 99-110.
17. R. Nagel and J. Poland, The critical spectrum of a strongly continuous semigroup, Adv. Math. 152 (2000), 120-133.
18. R. Nagel and E. Sinestrari, Inhomogenous Volterra integrodifferential equations for Hille-Yosida operators, in "Functional Analysis" (ed. K.D. Bierstedt, A. Pietsch, W.M. Ruess and D. Vogt), Lecture Notes in Pure and Appl. Math. 150, Marcel Dekker, 1994, 51-70.
19. T. Naito, N.V. Minh, R. Miyazaki and J.S. Shin, A decomposition theorem for bounded solutions and the existence of periodic solutions of periodic differential equations, J. Diff. Eq. 160 (2000), 263-282.
20. T. Naito, N.V. Minh and J.S. Shin, New spectral criteria for almost periodic solutions of evolution equations, Studia Math. 145 (2001), 97-111.
21. J.M.A.M. van Neerven, The Adjoint of a Semigroup of Linear Operators, Lect. Notes in Math., Vol. 1529, Springer-Verlag, 1992.
22. A. Neves, H. de Souza Ribeiro and O. Lopes, On the spectrum of evolution operators generated by hyperbolic systems, J. Funct. Anal. 67 (1986), 320-344.
23. G. Nickel, Evolution semigroups for nonautonomous Cauchy problems, Abstract Appl. Anal. 2 (1997), 73-95.
24. G. Nickel and A. Rhandi, On the essential spectral radius of semigroups generated by perturbations of Hille-Yosida operators, J. Diff. Int. Eq., to appear.
25. L. Paquet, Semigroupes généralisés et équations d'évolutions, Séminaire Théorie Potentiel Paris 4 (1979), 243-263.
26. A. V. Rezounenko, Inertial manifolds with delay for retarded semilinear parabolic equations, Disc. Cont. Dyn. Sys. 6 (2000), 829-840.
27. A. Rhandi, Extrapolation methods to solve non-autonomous retarded partial differential equations, Studia Math. 126 (1997), 219-233.
28. 1, Positivity 2 (1998), 101-113.
29. 1, Discrete and Continuous Dynamical Systems 6 (2000), 663-683.
30. W.M. Ruess, Existence of solutions to partial differential equations with delay, In: A. Kartsatos (ed.): Theory and applications of nonlinear operators of accretive and monotone type. Marcel Dekker Lect. Notes Pure Appl. Math. 178 (1996), 259-288.
31. R. Schnaubelt, Well-posedness and asymptotic behaviour of nonautonomous linear evolution equations, preprint(2001).
32. E. Sinestrari, Wave equation with memory, Discrete and Continuous Dynamical Systems 6 (2000), 881-896.
33. H.R. Thieme, Balanced exponential growth of operator semigroups, J. Math. Anal. Appl. 223 (1998), 30-49.
34. H.R. Thieme, Positive perturbations of operator semigroups: growth bounds, essential compactness, and asynchronous exponential growth, Disc. Cont. Dyn. Sys. 4 (1998), 753-764.
35. J. Wu, Theory and Applications of Partial Functional Differential Equations, Springer-Verlag, 1996.