Bi-spaces global attractors in abstract parabolic equations

• Autorzy: J. W. Cholewa , T. Dłotko
• Języki publikacji: EN

Abstrakty

EN

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 𝓐 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.

Kategorie tematyczne

• 35K15: Initial value problems for second-order parabolic equations
• 35B40: Asymptotic behavior of solutions
• 35K45: Initial value problems for second-order parabolic systems
• 35B41: Attractors

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2003
• Tom: 60
• Numer: 1
• Strony: 13-26

Daty

wydano

2003

Twórcy

autor

J. W. Cholewa

• Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland

autor

T. Dłotko

• Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland

Identyfikatory

DOI

10.4064/bc60-0-1