Asymptotic Smoothing and the Global Attractor of a Weakly Damped Kdv Equation on the Real Line
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چکیده
The existence of the global attractor of a weakly damped, forced Korteweg-de Vries equation in the phase space L(R) is proved. An optimal asymptotic smoothing effect of the equation is also shown, namely, that for forces in L(R), the global attractor in the phase space L(R) is actually a compact set in H(R). The energy equation method is used in conjunction with a suitable splitting of the solutions; the dispersive regularization properties of the equation in the context of Bourgain spaces are extensively exploited.
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تاریخ انتشار 2000