UNIFORM STABILIZATION OF A CLASS OF COUPLED SYSTEMS OF KDV EQUATIONS WITH LOCALIZED DAMPING

作者：Massarolo C P^*; Menzala G P; Pazoto A F

来源：Quarterly of Applied Mathematics, 2011, 69(4): 723-746.

• Exponential decay
• stabilization
• Korteweg-de Vries equation

We study the stabilization of solutions of a coupled system of Korteweg-de Vries (KdV) equations in a bounded interval under the effect of a localized damping term. We use multiplier techniques combined with the so-called "compactness-uniqueness argument". The problem is then reduced to proving a unique continuation property (UCP) for weak solutions. The exponential decay of solutions was previously obtained in Bisognin, Bisognin, and Menzala (2003) when the damping was effective simultaneously in neighborhoods of both extremes of the bounded interval. In this work we address the general case using a different approach to obtain the UCP and stabilize the system.

• 出版日期2011-12