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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access May 17, 2014

Local attractivity in nonautonomous semilinear evolution equations

  • Joël Blot EMAIL logo , Constantin Buşe and Philippe Cieutat

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

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Received: 2014-1-17
Accepted: 2014-3-21
Published Online: 2014-5-17
Published in Print: 2014-1-1

© 2014 Joël Blot et al.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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