Abstract parabolic problems in ordered Banach spaces

Alexandre N. Carvalho, Jan W. Cholewa, and Tomasz Dlotko. "Abstract parabolic problems in ordered Banach spaces." Colloquium Mathematicae 90.1 (2001): 1-17. <http://eudml.org/doc/283495>.

@article{AlexandreN2001,
abstract = {We consider abstract parabolic problems in ordered Banach spaces and give conditions under which they have global attractors. Our approach is via comparison of solutions. Within this approach abstract comparison principles are obtained and bounds on the attractors are given by order intervals in Banach spaces. These results are applied to ordinary differential equations and to parabolic equations for which the main part is given by a sum of fractional powers of sectorial operators having increasing resolvents and integral operators having positive kernels.},
author = {Alexandre N. Carvalho, Jan W. Cholewa, Tomasz Dlotko},
journal = {Colloquium Mathematicae},
keywords = {abstract comparison principles},
language = {eng},
number = {1},
pages = {1-17},
title = {Abstract parabolic problems in ordered Banach spaces},
url = {http://eudml.org/doc/283495},
volume = {90},
year = {2001},
}

TY - JOUR
AU - Alexandre N. Carvalho
AU - Jan W. Cholewa
AU - Tomasz Dlotko
TI - Abstract parabolic problems in ordered Banach spaces
JO - Colloquium Mathematicae
PY - 2001
VL - 90
IS - 1
SP - 1
EP - 17
AB - We consider abstract parabolic problems in ordered Banach spaces and give conditions under which they have global attractors. Our approach is via comparison of solutions. Within this approach abstract comparison principles are obtained and bounds on the attractors are given by order intervals in Banach spaces. These results are applied to ordinary differential equations and to parabolic equations for which the main part is given by a sum of fractional powers of sectorial operators having increasing resolvents and integral operators having positive kernels.
LA - eng
KW - abstract comparison principles
UR - http://eudml.org/doc/283495
ER -