Asymptotic stability of a Korteweg–de Vries equation with a two-dimensional center manifold
Local asymptotic stability analysis is conducted for an initial-boundary-value problem of a Korteweg–de Vries equation posed on a finite interval [0,2π7/3]{[0,2\pi\sqrt{7/3}]}. The equation comes with a Dirichlet boundary condition at the left end-point and both the Dirichlet and Neumann homogeneo...
Main Authors: | , , , |
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Format: | Article |
Language: | English |
Published: |
De Gruyter
2018-11-01
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Series: | Advances in Nonlinear Analysis |
Subjects: | |
Online Access: | https://doi.org/10.1515/anona-2016-0097 |
Summary: | Local asymptotic stability analysis is conducted for an initial-boundary-value problem of a Korteweg–de Vries
equation posed on a finite interval [0,2π7/3]{[0,2\pi\sqrt{7/3}]}.
The equation comes with a Dirichlet
boundary condition at the left end-point and both the Dirichlet and Neumann
homogeneous boundary conditions at the right end-point. It is known that the
associated linearized equation around the origin is
not asymptotically stable. In this paper, the nonlinear
Korteweg–de Vries equation is proved to be
locally asymptotically stable around the origin through the center
manifold method.
In particular, the existence of a two-dimensional local center manifold is presented, which is locally exponentially attractive. Analyzing the Korteweg–de Vries equation restricted on the local center manifold, we obtain a polynomial decay rate of the solution. |
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ISSN: | 2191-9496 2191-950X |