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Efendiyev, M.A. ; Zelik, S.*

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

Math. Meth. Appl. Sci. 32, 1638-1668 (2009)

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Open Access Green as soon as Postprint is submitted to ZB.

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We consider the following doubly nonlinear parabolic equation in a bounded domain Omega subset of R-3: f (x, partial derivative(t)u) = Delta(x)u - g (x, u) where the nonlinearity f is allowed to have a degeneracy with respect to partial derivative(t)u of the form partial derivative(t)u vertical bar partial derivative(t)u vertical bar(p) at some points x is an element of Omega. 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.

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