TEMPORAL GROWTH AND EVENTUAL PERIODICITY FOR DISPERSIVE WAVE EQUATIONS IN A QUARTER PLANE

被引：17
|
作者：
Bona, Jerry L. [1 ]
Wu, Jiahong [2 ]
机构：
[1] Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60601 USA
[2] Oklahoma State Univ, Dept Math, Stillwater, OK 74078 USA
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2009年 / 23卷 / 04期
基金：
美国国家科学基金会;
关键词：
Large-time behavior; eventual periodicity; KdV equation; BBM equation; BBM-Burgers equation; KdV-Burgers equation; DE-VRIES EQUATION; MODEL;
D O I：
10.3934/dcds.2009.23.1141
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Studied here is the large-time behavior and eventual periodicity of solutions of initial-boundary-value problems for the BBM equation and the KdV equation, with and without a Burgers-type dissipation appended. It is shown that the total energy of a solution of these problems grows at an algebraic rate which is in fact sharp for solutions of the associated linear equations. We also establish that solutions of the linear problems are eventually periodic if the boundary data are periodic.
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页码：1141 / 1168
页数：28
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