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Strong Global Attractors for 3D Wave Equations with Weakly Damping

DOI: 10.1155/2012/469382

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Abstract:

We consider the existence of the global attractor 1 for the 3D weakly damped wave equation. We prove that 1 is compact in (2(Ω)∩10(Ω))×10(Ω) and attracts all bounded subsets of (2(Ω)∩10(Ω))×10(Ω) with respect to the norm of (2(Ω)∩10(Ω))×10(Ω). Furthermore, this attractor coincides with the global attractor in the weak energy space 10(Ω)×2(Ω).

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