On the Well-posedness and Asymptotic Behavior of a Nonlinear Dispersive System in Weighted Spaces

On the Well-posedness and Asymptotic Behavior of a Nonlinear Dispersive System in Weighted Spaces This paper is concerned with a model for propagation of long waves in a channel generated by a wave maker mounted at one end. The mathematical structure consists in a coupled system of two nonlinear Korteweg-de Vries equations posed on the positive half line. Under the effect of a localized damping term it is shown that the solutions of the system are exponentially stable and globally well-posed in the weighted space L 2 (( x +1) m dx ) for m ≥1. The stabilization problem is studied constructing a Lyapunov function by induction on m and the well-posedness is obtained by passing to the limit in a sequence of solutions in L 2 ( e 2 bx dx ) for b >0. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

On the Well-posedness and Asymptotic Behavior of a Nonlinear Dispersive System in Weighted Spaces

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Publisher
Springer US
Copyright
Copyright © 2014 by Springer Science+Business Media New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-013-9220-6
Publisher site
See Article on Publisher Site

References

  • Decay of solutions to damped Korteweg-de Vries type equation
    Cavalcanti, M.M.; Cavalcanti, V.N.D.; Faminskii, A.; Natali, F.
  • Weak and strong interaction between internal solitary waves
    Gear, J.A.; Grimshaw, R.
  • On the uniform decay for the Korteweg-de Vries equation with weak damping
    Massarolo, C.P.; Menzala, G.P.; Pazoto, A.F.

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