| Texto completo | |
| Autor(es): |
Capistrano-Filho, Roberto de A.
;
Kwak, Chulkwang
;
Leal, Francisco J. Vielma
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS; v. 68, p. 42-pg., 2022-07-14. |
| Resumo | |
The local and global control results for a general higher-order KdV-type operator posed on the unit circle are presented. Using spectral analysis, we are able to prove local results, that is, the equation is locally controllable and exponentially stable. To extend the local results to the global one we captured the smoothing properties of the Bourgain spaces, the so-called propagation of regularity, which are proved with a new perspective. These propagation, together with the Strichartz estimates, are the key to extending the local control properties to the global one, precisely, higher-order KdV-type equations are globally controllable and exponentially stabilizable in the Sobolev space H-s(T) for any s >= 0. Our results recover previous results in the literature for the KdV and Kawahara equations and extend, for a general higher-order operator of KdV-type, the Strichartz estimates as well as the propagation results, which are the main novelties of this work. (C) 2022 Elsevier Ltd. All rights reserved. (AU) | |
| Processo FAPESP: | 20/14226-4 - Equações dispersivas: Controlabilidade e estabilização em dom1nios periódicos |
| Beneficiário: | Francisco Javier Vielma Leal |
| Modalidade de apoio: | Bolsas no Brasil - Pós-Doutorado |