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Inertial manifolds, symmetry and applications to PDE’s. (English) Zbl 0819.35075

Diaz, J.-I. (ed.) et al., Mathematics, climate and environment. Paris: Masson. Res. Notes Appl. Math. 27, 296-306 (1993).
Nonlinear parabolic equations in a small or thin bounded domain in \(\mathbb{R}^ 2\) with periodic, Neuman or Dirichlet boundary conditions are considered. Using inertial manifolds (under the spectral gap condition) and the group of symmetries of the equation the asymptotic behavior of the solutions of the equation is studied.
For the entire collection see [Zbl 0782.00023].
Reviewer: H.D.Voulov (Sofia)

MSC:

35K55 Nonlinear parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
58J70 Invariance and symmetry properties for PDEs on manifolds
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