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Exponential attractors for reaction-diffusion equations with arbitrary polynomial growth. (English) Zbl 1170.35349
Summary: We study exponential attractors for an equation with arbitrary polynomial growth nonlinearity f and inhomogeneous term g. First, we prove by the -trajectory method that the exponential attractor in L 2 (𝛺) with gH -1 (𝛺). Second, by proving the semigroup satisfying discrete squeezing property, we obtain the exponential attractor in H 0 1 (𝛺) with gL 2 (𝛺). Because the solutions without higher regularity than L 2p-2 (𝛺) for g belong only to L 2 (𝛺) in the equation, the general method by proving the Lipschitz continuity between L 2p-2 (𝛺) and L 2 (𝛺) does not work in our case. Therefore, we give a new method (presented in a theorem) to obtain an exponential attractor in a stronger topology space i.e., L 2p-2 (𝛺) with g𝔾 (stated in a definition) when it is out of reach for the other known techniques.
35B41Attractors (PDE)
35K57Reaction-diffusion equations