Reduction of dimension of approximate intertial manifolds by symmetry
| dc.contributor.author | Rodríguez Bernal, Aníbal | |
| dc.contributor.author | Wang, Bixiang | |
| dc.date.accessioned | 2023-06-20T17:09:12Z | |
| dc.date.available | 2023-06-20T17:09:12Z | |
| dc.date.issued | 1999-10 | |
| dc.description.abstract | In this paper, we study approximate inertial manifolds for nonlinear evolution partial differential equations which possess symmetry. The relationship between symmetry and dimensions of approximate inertial manifolds is established. We demonstrate that symmetry can reduce the dimensions of an approximate inertial manifold. Applications for concrete evolution equations are given. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | DGES | |
| dc.description.sponsorship | Ministerio de Educacion y Cultura | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/17979 | |
| dc.identifier.doi | 10.1017/S000497270003642X | |
| dc.identifier.issn | 0004-9727 | |
| dc.identifier.officialurl | http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=4831588 | |
| dc.identifier.relatedurl | http://journals.cambridge.org/action/login?sessionId=1D97595DB713FA150B5C9A401EC7FCB0.journals | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57854 | |
| dc.issue.number | 2 | |
| dc.journal.title | Bulletin of the Australian Mathematical Society | |
| dc.language.iso | eng | |
| dc.page.final | 330 | |
| dc.page.initial | 319 | |
| dc.publisher | Cambridge University Press | |
| dc.relation.projectID | PB96-0648 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.98 | |
| dc.subject.keyword | Global dynamical properties | |
| dc.subject.keyword | Inertial manifolds | |
| dc.subject.keyword | Equations | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.title | Reduction of dimension of approximate intertial manifolds by symmetry | |
| dc.type | journal article | |
| dc.volume.number | 60 | |
| dcterms.references | Foias, C., Jolly, M.S., Kevrekidis, I.G., Sell, G.R. and Titi, E.S., ‘On the computation of inertial manifolds’, Physics Lett. A 131 (1988), 433–436. Foias, C., Sell, G.R. and Temam, R., ‘Inertial manifolds for nonlinear evolutionary equations’, J. Differential Equations 73 (1988), 309–353. Foias, C., Sell, G.R. and Titi, E.S., ‘Exponential tracking and approximation of inertial manifolds for dissipative equations’, J. Dynamics Differential Eqations 1 (1989), 199–244. Hale, J.K., Asymptotic behaviour of dissipative systems, Math. Surveys and Monographs 25 (American Mathematical Society, Providence, R.I., 1988). Il′yashenko, Ju., ‘Global analysis of the phase portrait for the Kuramoto-Sivashinsky equation’, J. Dynamics Differential Equations 4 (1992), 585–615. Jolly, M.S., Kevrekidis, I.G. and Titi, E.S., ‘Approximate inertial manifolds for the Kuramoto-Sivashinsky equation: analysis and computations’, Phys. D. 44 (1990), 38–60. Nicolaenko, B., Sheurer, B. and Temam, R., ‘Some global dynamical properties of the Kuramoto-Sivashinsky equation: nonlinear stability and attractors’, Phys. D. 16 (1985). 155–183. Nicolaenko, B., Sheurer, B. and Temam, R., ‘Dynamical properties of a class of pattern formation equations’. Comm. Partial Differential Eqations 14 (1989), 245–297. Rodriguez-Bernal, A., ‘Inertial manifolds for dissipative semiflows in Banach spaces’, Appl. Anal. 37 (1990), 95–141. Rodriguez-Bernal, A., ‘On the construction of inertial manifolds under symmetry constraints I: abstract results’, Nonlinear Anal. 19 (1992), 687–700. Rodriguez-Bernal, A., ‘On the construction of inertial manifolds under symmetry constraints II: O(2) constraint and inertial manifolds on thin domains’, J. Math. Pures Appl. 72 (1993), 57–79. Sell, G.R., ‘An optimality condition for approximate inertial manifolds’, in Turbulence in fluid flows: A dynamical system approach (Springer-Verlag, Berlin, Heidelberg, New York, 1993), pp. 165–186. Stuart, A.M., ‘Perturbation theory for infinite dimensional dynamical systems’, in Theory and numerics of ordinary and partial differential equations, (Ainsworth, M. et al., Editors) (Oxford University Press, 1995). Temam, R., Infinite dimensional dynamical systems in mechanics and physics. (Springer-Verlag, Berlin, Heidelberg, New York, 1988). | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | fb7ac82c-5148-4dd1-b893-d8f8612a1b08 | |
| relation.isAuthorOfPublication.latestForDiscovery | fb7ac82c-5148-4dd1-b893-d8f8612a1b08 |
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