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The existence of compact exponential attracting set for dynamical system. (English) Zbl 1184.35069

Summary: Using the measure of noncompactness, we obtain the existence of compact exponential attracting set for general dynamical system. Then we give a method for proving the existence of compact exponential attracting set.

MSC:

35B41 Attractors
35K57 Reaction-diffusion equations
35B40 Asymptotic behavior of solutions to PDEs
35K58 Semilinear parabolic equations
35K20 Initial-boundary value problems for second-order parabolic equations
35K90 Abstract parabolic equations
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