Titlebook: Attractors for infinite-dimensional non-autonomous dynamical systems; Alexandre N. Carvalho,José A. Langa,James C. Robin Book 2013 Springe

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G Protein-Coupled Receptor Screening Assayschapter we illustrate the results of Chaps. 2 and 4 by driving the dynamics with a non-autonomous forcing term. With such an equation, which has no clear underlying structure (like a Lyapunov function, for example), the application of the more ‘global’ results of these two chapters (existence of a f

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https://doi.org/10.1007/978-1-4939-2336-6 to compare the asymptotic dynamics of systems with different ‘parameter values’ by comparing their attractors and the flow on them. We assume that . and converges to a continuously differentiable function . as ε goes to zero. For this problem we prove that the attractors are continuous at ε = 0 and

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Chenyi Liao,Victor May,Jianing Lipyzhov and Vishik (2002) [see also the appendix in the book by Vishik (1992)]. Reinterpreted in the language of processes, the uniform attractor is the minimal fixed (time-independent) compact subset . of the phase space that attracts all trajectories uniformly for bounded sets . of initial conditio

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https://doi.org/10.1007/978-1-4939-1218-6In 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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https://doi.org/10.1007/978-1-4939-2336-6In this chapter we consider the asymptotic dynamics of parabolic problems of the form . where . is a positive integer, . is a bounded domain with smooth boundary ., ., ., and . is measurable in the first variable and locally Lipschitz in the second and third variables, uniformly for ..

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