Asymptotic stability of a Korteweg–de Vries equation with a two-dimensional center manifold
Asymptotic stability of a Korteweg–de Vries equation with a two-dimensional center manifold
Abstract Local asymptotic stability analysis is conducted for an initial-boundary-value problem of a Korteweg–de Vries equation posed on a finite interval <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo>[</m:mo> <m:mn>0</m:mn> <m:mo>,</m:mo> <m:mrow> <m:mn>2</m:mn> <m:mo></m:mo> <m:mi>π</m:mi> <m:mo></m:mo> <m:msqrt> <m:mrow> <m:mn>7</m:mn> <m:mo>/</m:mo> <m:mn>3</m:mn> </m:mrow> </m:msqrt> </m:mrow> <m:mo>]</m:mo> </m:mrow> </m:math> {[0,2\pi\sqrt{7/3}]} . The equation comes with a …