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

We consider the following doubly nonlinear parabolic equation in a bounded domain Ω??³: where the nonlinearity f is allowed to have a degeneracy with respect to ?_tu of the form ?_tu|?_tu|^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.