Asymptotic behavior of the Korteweg-de Vries equation

Ademir F. Pazoto | Linares, Felipe

Keywords: Exponential Decay | stabilization | Korteweg-de Vries equation

The purpose of this work is to study the exponential stabilization of the Korteweg-de Vries equation in the right half-line under the effect of a localized damping term. We follow the methods in \cite{mvz} which combine multiplier techniques and compactness arguments and reduce the problem to prove the unique continuation property of weak solutions. Here, the unique continuation is obtained in two steps: we first prove that solutions vanishing on any subinterval are necessarily smooth and then we apply the unique continuation results proved in \cite{ss}. In particular, we show that the exponential rate of decay is uniform in bounded sets of initial data.

Anexos:

• kdv-quarter3.pdf