On the control issues for higher-order nonlinear dispersive equations on the circle
- 주제(키워드) Bourgain spaces , Control problems , KdV-type equation , Propagation of regularity/compactness
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- OA유형 All Open Access, Green
- 발행기관 Elsevier Ltd
- 발행년도 2022
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000193378
- 본문언어 영어
- Published As https://doi.org/10.1016/j.nonrwa.2022.103695
초록/요약
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 Hs(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. © 2022 Elsevier Ltd
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