# Bi-spaces global attractors in abstract parabolic equations

Banach Center Publications (2003)

- Volume: 60, Issue: 1, page 13-26
- ISSN: 0137-6934

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topJ. W. Cholewa, and T. Dłotko. "Bi-spaces global attractors in abstract parabolic equations." Banach Center Publications 60.1 (2003): 13-26. <http://eudml.org/doc/281886>.

@article{J2003,

abstract = {An abstract semilinear parabolic equation in a Banach space X is considered. Under general assumptions on nonlinearity this problem is shown to generate a bounded dissipative semigroup on $X^α$. This semigroup possesses an $(X^α - Z)$-global attractor that is closed, bounded, invariant in $X^α$, and attracts bounded subsets of $X^α$ in a ’weaker’ topology of an auxiliary Banach space Z. The abstract approach is finally applied to the scalar parabolic equation in Rⁿ and to the partly dissipative system.},

author = {J. W. Cholewa, T. Dłotko},

journal = {Banach Center Publications},

keywords = {partly dissipative system; Cauchy problem; global solution; absorbing set; invariant attracting set},

language = {eng},

number = {1},

pages = {13-26},

title = {Bi-spaces global attractors in abstract parabolic equations},

url = {http://eudml.org/doc/281886},

volume = {60},

year = {2003},

}

TY - JOUR

AU - J. W. Cholewa

AU - T. Dłotko

TI - Bi-spaces global attractors in abstract parabolic equations

JO - Banach Center Publications

PY - 2003

VL - 60

IS - 1

SP - 13

EP - 26

AB - An abstract semilinear parabolic equation in a Banach space X is considered. Under general assumptions on nonlinearity this problem is shown to generate a bounded dissipative semigroup on $X^α$. This semigroup possesses an $(X^α - Z)$-global attractor that is closed, bounded, invariant in $X^α$, and attracts bounded subsets of $X^α$ in a ’weaker’ topology of an auxiliary Banach space Z. The abstract approach is finally applied to the scalar parabolic equation in Rⁿ and to the partly dissipative system.

LA - eng

KW - partly dissipative system; Cauchy problem; global solution; absorbing set; invariant attracting set

UR - http://eudml.org/doc/281886

ER -

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