Abstract parabolic problems in ordered Banach spaces

Volume 90 / 2001

Alexandre N. Carvalho, Jan W. Cholewa, Tomasz Dlotko Colloquium Mathematicum 90 (2001), 1-17 MSC: Primary 35K90; Secondary 35S15, 35B40, 35B41. DOI: 10.4064/cm90-1-1

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.

Authors

  • Alexandre N. CarvalhoDepartamento 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
    e-mail
  • Jan W. CholewaInstitute of Mathematics
    Silesian University
    40-007 Katowice, Poland
    e-mail
  • Tomasz DlotkoInstitute of Mathematics
    Silesian University
    40-007 Katowice, Poland
    e-mail

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