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Partly dissipative systems in uniformly local spaces

100%

Carvalho A., Dlotko T.

Colloquium Mathematicum

2004

tom 100

nr 2

221-242

We study the existence of attractors for partly dissipative systems in ℝⁿ. For these systems we prove the existence of global attractors with attraction properties and compactness in a slightly weaker topology than the topology of the phase space. We obtain abstract results extending the usual theory to encompass such two-topologies attractors. These results are applied to the FitzHugh-Nagumo equations in ℝⁿ and to Field-Noyes equations in ℝ. Some embeddings between uniformly local spaces are also proved.

Abstract parabolic problems in ordered Banach spaces

81%

Carvalho A., Cholewa J., Dlotko T.

Colloquium Mathematicum

2001

tom 90

nr 1

1-17

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.

Ograniczanie wyników

2 Colloquium Mathematicum

2 Carvalho A.

2 Dlotko T.

1 Cholewa J.

1 2004

1 2001

Wyniki wyszukiwania

Partly dissipative systems in uniformly local spaces

Abstract parabolic problems in ordered Banach spaces