Geodesic
Compact attractor for weakly damped driven Korteweg-de Vries equations on the real line
Czechoslovak Mathematical Journal, Tome 48 (1998) no. 1, pp. 85-94

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We investigate the long-time behaviour of solutions to the Korteweg-de Vries equation with a zero order dissipation and an additional forcing term, when the space variable varies over $R$, and prove that it is described by a maximal compact attractor in $H^2(R)$.
Classification : 35B40, 35Q53, 47H20, 58F39
Keywords: Korteweg-de Vries equation; attractor; unbounded domain. 
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     author = {Lauren\c{c}ot, Ph.},
     title = {Compact attractor for weakly damped driven {Korteweg-de} {Vries} equations on the real line},
     journal = {Czechoslovak Mathematical Journal},
     pages = {85--94},
     publisher = {mathdoc},
     volume = {48},
     number = {1},
     year = {1998},
     mrnumber = {1614084},
     zbl = {0928.35145},
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     url = {http://geodesic.mathdoc.fr/item/CMJ_1998__48_1_a7/}
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Laurençot, Ph. Compact attractor for weakly damped driven Korteweg-de Vries equations on the real line. Czechoslovak Mathematical Journal, Tome 48 (1998) no. 1, pp. 85-94. http://geodesic.mathdoc.fr/item/CMJ_1998__48_1_a7/