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Finite-dimensional attractors and exponential attractors for degenerate doubly nonlinear equations

✍ Scribed by M. Efendiev; S. Zelik

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
244 KB
Volume
32
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

We consider the following doubly nonlinear parabolic equation in a bounded domain Ω⊂ℝ^3^:

where the nonlinearity f is allowed to have a degeneracy with respect to ∂~t~u of the form ∂~t~u|∂~t~u|^p^ at some points x∈Ω.

Under some natural assumptions on the nonlinearities f and g, we prove the existence and uniqueness of a solution of that problem and establish the finite‐dimensionality of global and exponential attractors of the semigroup associated with this equation in the appropriate phase space. Copyright © 2009 John Wiley & Sons, Ltd.

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