descriptionPublicationkeyboard_double_arrow_right Article 16 Jan 2009 English Publisher:WileyJournal:Mathematical Methods in the Applied Sciences, volume 32, pages 1,638-1,668 (issn: 0170-4214, eissn: 1099-1476,

Authors: Efendiev, M; Zelik, S;

doi: 10.1002/mma.1102

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

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Abstract

AbstractWe consider the following doubly nonlinear parabolic equation in a bounded domain Ω⊂ℝ3:where the nonlinearityfis allowed to have a degeneracy with respect to ∂tuof the form ∂tu|∂tu|pat some pointsx∈Ω.Under some natural assumptions on the nonlinearitiesfandg, 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.

Related Organizations

University of Surrey
United Kingdom
Technical University of Munich
Germany

Keywords

exponential attractors, Initial-boundary value problems for second-order parabolic equations, Nonlinear parabolic equations, Degenerate parabolic equations, doubly nonlinear equation, degenerate parabolic PDE, Attractors of solutions to ordinary differential equations

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