The initial-boundary value problem for the Kawahara equation on the half-line
- 주제(키워드) Initial-boundary value problem , Kawahara equation , Local well-posedness
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- OA유형 Green Submitted
- 발행기관 Birkhauser
- 발행년도 2020
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000168821
- 본문언어 영어
- Published As https://dx.doi.org/10.1007/s00030-020-00648-6
초록/요약
This paper concerns the initial-boundary value problem of the Kawahara equation posed on the right and left half-lines. We prove the local well-posedness in the low regularity Sobolev space. We introduce the Duhamel boundary forcing operator, which is introduced by Colliander and Kenig (Commun Partial Differ Equ 27:2187–2266, 2002) in the context of Airy group operators, to construct solutions on the whole line. We also give the bilinear estimate in Xs,b space for b<12, which is almost sharp compared to IVP of Kawahara equation (Chen et al. in J Anal Math 107:221–238, 2009; Jia and Huo in J Differ Equ 246:2448–2467, 2009). © 2020, Springer Nature Switzerland AG.
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