Geodesic
Abstract parabolic problems in ordered Banach spaces
Alexandre N. Carvalho1 ; Jan W. Cholewa2 ; Tomasz Dlotko2
1 Departamento de Matemática Instituto de Ciências Matemáticas e de Computação Universidade de São Paulo Campus de São Carlos, Caixa Postal 668 13.560-970 São Carlos SP, Brazil
2 Institute of Mathematics Silesian University 40-007 Katowice, Poland
Colloquium Mathematicum, Tome 90 (2001) no. 1, pp. 1-17

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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.
DOI : 10.4064/cm90-1-1
Keywords: consider abstract parabolic problems ordered banach spaces conditions under which have global attractors approach via comparison solutions within approach abstract comparison principles obtained bounds attractors given order intervals banach spaces these results applied ordinary differential equations parabolic equations which main part given sum fractional powers sectorial operators having increasing resolvents integral operators having positive kernels

Alexandre N. Carvalho 1 ; Jan W. Cholewa 2 ; Tomasz Dlotko 2

1 Departamento de Matemática Instituto de Ciências Matemáticas e de Computação Universidade de São Paulo Campus de São Carlos, Caixa Postal 668 13.560-970 São Carlos SP, Brazil
2 Institute of Mathematics Silesian University 40-007 Katowice, Poland 
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Alexandre N. Carvalho; Jan W. Cholewa; Tomasz Dlotko. Abstract parabolic problems in ordered
Banach spaces. Colloquium Mathematicum, Tome 90 (2001) no. 1, pp. 1-17. doi: 10.4064/cm90-1-1

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