Displaying similar documents to “Stabilization of a wave-wave system.”

Unique continuation and decay for the Korteweg-de Vries equation with localized damping

Ademir Fernando Pazoto (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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This work is devoted to prove the exponential decay for the energy of solutions of the Korteweg-de Vries equation in a bounded interval with a localized damping term. Following the method in Menzala (2002) which combines energy estimates, multipliers and compactness arguments the problem is reduced to prove the unique continuation of weak solutions. In Menzala (2002) the case where solutions vanish on a neighborhood of both extremes of the bounded interval where equation holds was solved...

Stability and Instability of Solitary Wave Solutions of a Nonlinear Dispersive System of Benjamin-Bona-Mahony Type

Hakkaev, Sevdzhan (2003)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 35B35, 35B40, 35Q35, 76B25, 76E30. This paper concerns the orbital stability and instability of solitary waves of the system of coupling equations of Benjamin-Bona-Mahony type. By applying the abstract results of Grillakis, Shatah and Strauss and detailed spectral analysis, we obtain the existence and stability of the solitary waves. Partially Supported by Grant MM-810/98 of MESC and by Scientefic Research Grant 19/12.03.2003...