Bi-spaces global attractors in abstract parabolic equations

J. 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 -