Loading...
The Korteweg-de Vries equation on an interval
Himonas, A. Alexandrou Mantzavinos, Dionyssios Yan, Fangchi
Himonas, A. Alexandrou
Mantzavinos, Dionyssios
Yan, Fangchi
Citations
Altmetric:
Abstract
The initial-boundary value problem (IBVP) for the Korteweg-de Vries (KdV) equation on an interval is studied by extending a novel approach recently developed for the well-posedness of the KdV on the half-line, which is based on the solution formula produced via Fokas’ unified transform method for the associated forced linear IBVP. Replacing in this formula the forcing by the nonlinearity and using data in Sobolev spaces suggested by the space-time regularity of the Cauchy problem of the linear KdV gives an iteration map for the IBVP which is shown to be a contraction in an appropriately chosen solution space. The proof relies on key linear estimates and a bilinear estimate similar to the one used for the KdV Cauchy problem by Kenig, Ponce, and Vega.
Description
This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in J. Math. Phys. 60, 051507 (2019) and may be found at https://doi.org/10.1063/1.5080366.
Date
2019-05-08
Journal Title
Journal ISSN
Volume Title
Publisher
American Institute of Physics
Collections
Research Projects
Organizational Units
Journal Issue
Keywords
Citation
J. Math. Phys. 60, 051507 (2019); https://doi.org/10.1063/1.5080366