Local attractivity in nonautonomous semilinear evolution equations

Joël Blot; Constantin Buşe; Philippe Cieutat

Nonautonomous Dynamical Systems (2014)

  • Volume: 1, Issue: 1, page 72-82, electronic only
  • ISSN: 2353-0626

Abstract

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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

How to cite

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Joël Blot, Constantin Buşe, and Philippe Cieutat. "Local attractivity in nonautonomous semilinear evolution equations." Nonautonomous Dynamical Systems 1.1 (2014): 72-82, electronic only. <http://eudml.org/doc/266550>.

@article{JoëlBlot2014,
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},
author = {Joël Blot, Constantin Buşe, Philippe Cieutat},
journal = {Nonautonomous Dynamical Systems},
keywords = {semilinear evolution equation; evolution family; exponential stability; attractivity; Nemytskii operator},
language = {eng},
number = {1},
pages = {72-82, electronic only},
title = {Local attractivity in nonautonomous semilinear evolution equations},
url = {http://eudml.org/doc/266550},
volume = {1},
year = {2014},
}

TY - JOUR
AU - Joël Blot
AU - Constantin Buşe
AU - Philippe Cieutat
TI - Local attractivity in nonautonomous semilinear evolution equations
JO - Nonautonomous Dynamical Systems
PY - 2014
VL - 1
IS - 1
SP - 72
EP - 82, electronic only
AB - 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
LA - eng
KW - semilinear evolution equation; evolution family; exponential stability; attractivity; Nemytskii operator
UR - http://eudml.org/doc/266550
ER -

References

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