Pullback exponential attractors for nonautonomous equations Part I: Semilinear parabolic problems |
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Authors: | Radoslaw Czaja Messoud Efendiev |
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Affiliation: | a CAMGSD, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal b Helmholtz Center Munich, Institute of Biomathematics and Biometry, Ingolstädter Landstraße 1, 85764 Neuherberg, Germany |
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Abstract: | A family of compact and positively invariant sets with uniformly bounded fractal dimension which at a uniform exponential rate pullback attract bounded subsets of the phase space under the process is constructed. The existence of such a family, called a pullback exponential attractor, is proved for a nonautonomous semilinear abstract parabolic Cauchy problem. Specific examples will be presented in the forthcoming Part II of this work. |
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Keywords: | Exponential attractor Pullback attractor Fractal dimension Nonautonomous dynamical systems |
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