Journal of Dynamics and Differential Equations

, Volume 31, Issue 2, pp 1029–1039 | Cite as

Determining Nodes for the Damped Forced Periodic Korteweg-de Vries Equation

  • Olivier GoubetEmail author


We show that solutions of the periodic KdV equations
$$\begin{aligned} u_t+\gamma u +u_{xxx}+uu_x=f, \end{aligned}$$
are asymptotically determined by their values at three points. That is if there exists \(x_1,x_2,x_3\) such that \(0< x_3-x_2<<x_3-x_1<<1\) and
$$\begin{aligned} \lim _{t\rightarrow +\infty } |u_1(t,x_j)-u_2(t,x_j)|=0, \; \mathrm{for} \; j=1,2,3, \end{aligned}$$
for two solutions \(u_1,u_2\) of the KdV equation above, then
$$\begin{aligned} \lim _{t\rightarrow +\infty }||u_1(t)-u_2(t)||_{H^1}=0. \end{aligned}$$


Damped forced KdV equations Global attractor Determining nodes 

Mathematics Subject Classification

35Q53 37L50 35B41 



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Authors and Affiliations

  1. 1.LAMFA, UMR CNRS 7352Université de Picardie Jules VerneAmiens CedexFrance

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