# 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

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topJoël 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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- [8] G.M. N’Guérékata, Almost automorphic and almost periodic functions in abstract spaces, Kluwer Academic Publishers, New York, 2001.
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