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.
Applied Mathematics and Optimization – Springer Journals
Published: Feb 1, 2014
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