Families of Periodic Solutions for Some Hamiltonian PDEs

被引：6

作者：

Arioli, Gianni ^{[1
]}

Koch, Hans ^{[2
]}

机构：

[1] Politecn Milan, Dept Math, Piazza Leonardo da Vinci 32, I-20133 Milan, Italy

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

来源：

SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS | 2017年 / 16卷 / 01期

关键词：

periodic solutions; Hamiltonian PDEs; computer-assisted proof; PARTIAL-DIFFERENTIAL-EQUATIONS; COMPUTER-ASSISTED PROOF; ASYMMETRIC BEAM EQUATION; FREE-VIBRATIONS; SUSPENSION BRIDGES; RIGOROUS NUMERICS; EXISTENCE;

D O I：

10.1137/16M1070177

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the nonlinear wave equation u(tt) - u(xx) = +/- u(3) and the beam equation u(tt) + u(xxxx) = +/- u(3) on an interval. Numerical observations indicate that time-periodic solutions for these equations are organized into structures that resemble branches and seem to undergo bifurcations. In addition to describing our observations, we prove the existence of time-periodic solutions for various periods (a set of positive measure in the case of the beam equation) along the main nontrivial "branch." Our proofs are computer-assisted.

引用

页码：1 / 15

页数：15

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