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| GLOBAL DYNAMICS OF DISSIPATIVE GENERALIZED KORTEWEG-DE VRIES EQUATIONS |
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Citation： |
You Yuncheng.GLOBAL DYNAMICS OF DISSIPATIVE GENERALIZED KORTEWEG-DE VRIES EQUATIONS[J].Chinese Annals of Mathematics B,1996,17(4):389~402 |
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Net amount： 739 |
Authors： |
You Yuncheng; |
Foundation： |
the National Natural Science Foundation of China |
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| Abstract： |
This work deals with the dissipative generalized Korteweg-de Vries (gKdV) equations of the form $$\align &u_t + u^2 u_x + u_{xxx}-bu_{xx}+ ru = f,\quad t\geq 0, \\ &u(0,x) = u_0(x)\in V = H_{2\pi}^2, \endalign$$ with periodic boundary conditions. It is proved that there exists an inertial manifold for the semiflow generated by this equation in space $V$. Since such a
manifold is finite dimensional, positively invariant, and exponentially attracting of all the solution trajectories, the long-time dynamics of the dissipative gKdV equations are determined by a finite number of modes without the soliton phenomena. |
Keywords： |
Dissipative generalized KdV equation, Global dynamics,
Inertial manifold,Soliton |
Classification： |
35B40, 35Q53, 58F12, 76B15 |
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