Integration of Dissipative Partial Differential Equations: A Case Study

被引：42

作者：

Arioli, Gianni ^{[1
,2
]}

koch, Hans ^{[3
]}

机构：

[1] Politecn Milan, Dipartimento Matemat, I-20133 Milan, Italy

[2] Politecn Milan, MOX, I-20133 Milan, Italy

[3] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

来源：

SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS | 2010年 / 9卷 / 03期

关键词：

Kuramoto-Sivashinski equation; hyperbolicity; periodic orbit; computer-assisted proof; COVERING RELATIONS; SIVASHINSKY;

D O I：

10.1137/10078298X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We develop a computer-assisted technique for constructing and analyzing orbits of dissipative evolution equations. As a case study, the methods are applied to the Kuramoto-Sivashinski equation, for which we prove the existence of a hyperbolic periodic orbit.

引用

页码：1119 / 1133

页数：15

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