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Nonautonomous Dynamical Systems

formerly Nonautonomous and Stochastic Dynamical Systems

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2353-0626
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Local attractivity in nonautonomous semilinear evolution equations

Joël Blot
  • Corresponding author
  • Laboratoire SAMM EA 4543, Université Paris 1 Panthéon-Sorbonne, centre P.M.F., 90 rue de Tolbiac, 75634 Paris cedex 13, France
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/ Constantin Buşe / Philippe Cieutat
  • Laboratoire de Mathématiques de Versailles, UMR-CNRS 8100, Université Versailles-Saint-Quentin-en-Yvelines, 45 avenue des États-Unis, 78035 Versailles cedex, France
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Published Online: 2014-05-17 | DOI: https://doi.org/10.2478/msds-2014-0002

Abstract

We study the local attractivity of mild solutions of equations in the form u’(t) = A(t)u(t) + f (t, u(t)), where A(t) are (possible) unbounded linear operators in a Banach space and where f is a (possible) nonlinear mapping. Under conditions of exponential stability of the linear part, we establish the local attractivity of various kinds of mild solutions. To obtain these results we provide several results on the Nemytskii operators on the space of the functions which converge to zero at infinity

Keywords: semilinear evolution equation; evolution family; exponential stability; attractivity; Nemytskii operator

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About the article

Received: 2014-01-17

Accepted: 2014-03-21

Published Online: 2014-05-17

Published in Print: 2014-01-01


Citation Information: Nonautonomous Dynamical Systems, ISSN (Online) 2353-0626, DOI: https://doi.org/10.2478/msds-2014-0002.

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© 2014 Joël Blot et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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