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Part of the book series: Applied Mathematical Sciences ((AMS,volume 182))

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Abstract

In this chapter we develop the existence theory for pullback attractors in a way that recovers well known results for the global attractors of autonomous systems as a particular case (see, for example, Babin and Vishik 1992; Chepyzhov and Vishik 2002;Cholewa and Dlotko 2000; Chueshov 1999; Hale 1988; Ladyzhenskaya 1991; Robinson 2001; Temam 1988).

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Notes

  1. 1.

    Note that this is the classical definition of asymptotic compactness for a semigroup (e.g. Ladyzhenskaya 1991; Temam 1988), which is stronger (it implies boundedness) than the one in Hale (1988) or Raugel (2002) in which one also must assume that {T(t k )x k } is bounded.

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Carvalho, A.N., Langa, J.A., Robinson, J.C. (2013). Existence results for pullback attractors. In: Attractors for infinite-dimensional non-autonomous dynamical systems. Applied Mathematical Sciences, vol 182. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4581-4_2

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