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Inertial manifolds and finite-dimensional reduction for dissipative PDEs

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 نشر من قبل Sergey Zelik V.
 تاريخ النشر 2013
  مجال البحث
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 تأليف Sergey Zelik




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These notes are devoted to the problem of finite-dimensional reduction for parabolic PDEs. We give a detailed exposition of the classical theory of inertial manifolds as well as various attempts to generalize it based on the so-called Mane projection theorems. The recent counterexamples which show that the underlying dynamics may be in a sense infinite-dimensional if the spectral gap condition is violated as well as the discussion on the most important open problems are also included.



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