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1997 | 126 | 3 | 219-233
Tytuł artykułu

Extrapolation methods to solve non-autonomous retarded partial differential equations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Using extrapolation spaces introduced by Da Prato-Grisvard and Nagel we prove a non-autonomous perturbation theorem for Hille-Yosida operators. The abstract result is applied to non-autonomous retarded partial differential equations.
Słowa kluczowe
Czasopismo
Rocznik
Tom
126
Numer
3
Strony
219-233
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-03-25
Twórcy
  • AGFA, Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany, rhandi@casanet.net.ma
  • Département de Mathématiques, Université Cadi Ayyad, B.P.: S.15, 40000 Marrakech, Maroc
Bibliografia
  • [Am] H. Amann, Linear and Quasilinear Parabolic Problems, Birkhäuser, Basel, 1995.
  • [Bu-Be] P. Butzer and H. Berens, Semigroups of Operators and Approximation, Springer, Berlin, 1967.
  • [Cl] P. Clément et al., One-Parameter Semigroups, CWI Monographs 5, Amsterdam, 1987.
  • [Cl1] P. Clément, O. Diekmann, M. Gyllenberg, H. J. A. M. Heijmans, and H. R. Thieme, Perturbation theory for dual semigroups. I. The sun-reflexive case, Math. Ann. 277 (1987), 709-725.
  • [Cl2] P. Clément, O. Diekmann, M. Gyllenberg, H. J. A. M. Heijmans and H. R. Thieme, Perturbation theory for dual semigroups. II. Time-dependent perturbations in the sun-reflexive case, Proc. Roy. Soc. Edinburgh Sect. A 109 (1988), 145-172.
  • [DaP-G] G. Da Prato and P. Grisvard, On extrapolation spaces, Rend. Accad. Naz. Lincei 72 (1982), 330-332.
  • [Da-Sch-Zh] W. Desch, W. Schappacher, and K. P. Zhang, Semilinear evolution equations, Houston J. Math. 15 (1989), 527-552.
  • [Di-vGi-Lu-Wa] O. Diekmann, S. A. van Gils, S. M. Verduyn Lunel and H.-O. Walther, Delay Equations, Functional-, Complex- and Nonlinear Analysis, Springer, 1995.
  • [Go] J. A. Goldstein, Semigroups of Linear Operators and Applications, Oxford University Press, New York, 1985.
  • [Ha] J. K. Hale, Theory of Functional Differential Equations, Springer, 1977.
  • [Hi-Ph] E. Hille and R. S. Phillips, Functional Analysis and Semi-Groups, Amer. Math. Soc., Providence, 1957.
  • [Li] J. L. Lions, Théorèmes de trace et d'interpolation, I, Ann. Scuola Norm. Sup. Pisa 13 (1959), 389-403.
  • [Lu] A. Lunardi, Interpolation spaces between domains of elliptic operators and spaces of continuous functions with applications to nonlinear parabolic equations, Math. Nachr. 121 (1985), 295-318.
  • [Lu1] A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhäuser, Basel, 1995.
  • [Na] R. Nagel (ed.), One-Parameter Semigroups of Positive Operators, Lecture Notes in Math. 1184, Springer, 1986.
  • [Na1] R. Nagel (ed.), Sobolev spaces and semigroups, Semesterbericht Funktionalanalysis Tübingen (Sommersemester 1983), 1-19.
  • [Na2] R. Nagel and E. Sinestrari, Inhomogeneous Volterra integrodifferential equations for Hille-Yosida operators, in: Lecture Notes in Pure and Appl. Math. 150, Marcel Dekker, 1994, 51-70.
  • [vNe] J. van Neerven, The Adjoint of a Semigroup of Linear Operators, Lecture Notes in Math. 1529, Springer, 1992.
  • [Ni-Rh] G. Nickel and A. Rhandi, On the essential spectral radius of semigroups generated by perturbations of Hille-Yosida operators, Differential Integral Equations, to appear.
  • [Pa] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, 1983.
  • [Ta] H. Tanabe, Equations of Evolution, Pitman, London, 1979.
  • [Wa] T. Walther, Störungstheorie von Generatoren und Favard-Klassen, Dissertation, Tübingen, 1986.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv126i3p219bwm
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