| Full text | |
| Author(s): |
Total Authors: 3
|
| Affiliation: | [1] Vrije Univ Amsterdam, De Boelelaan 1081, NL-1081 HV Amsterdam - Netherlands
[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil
[3] McGill Univ, Dept Math & Stat, 805 Sherbrooke St W, Montreal, PQ H3A 0B9 - Canada
Total Affiliations: 3
|
| Document type: | Journal article |
| Source: | Archive for Rational Mechanics and Analysis; v. 228, n. 1, p. 129-157, APR 2018. |
| Web of Science Citations: | 5 |
| Abstract | |
In this paper, we develop computer-assisted techniques for the analysis of periodic orbits of ill-posed partial differential equations. As a case study, our proposed method is applied to the Boussinesq equation, which has been investigated extensively because of its role in the theory of shallow water waves. The idea is to use the symmetry of the solutions and a Newton-Kantorovich type argument (the radii polynomial approach) to obtain rigorous proofs of existence of the periodic orbits in a weighted a{''}{''}(1) Banach space of space-time Fourier coefficients with exponential decay. We present several computer-assisted proofs of the existence of periodic orbits at different parameter values. (AU) | |
| FAPESP's process: | 16/08704-5 - Rigorous computations in dynamics |
| Grantee: | Marcio Fuzeto Gameiro |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 16/21032-6 - Analysis of fluid dynamics data via persistent homology |
| Grantee: | Marcio Fuzeto Gameiro |
| Support Opportunities: | Scholarships abroad - Research |
| FAPESP's process: | 13/50382-7 - Rigorous computations for nonlinear partial differential equations |
| Grantee: | Marcio Fuzeto Gameiro |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 13/07460-7 - Rigorous computations for PDEs |
| Grantee: | Marcio Fuzeto Gameiro |
| Support Opportunities: | Regular Research Grants |