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.
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页码：1 / 15
页数：15
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