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Well-Posedness of a Higher Dispersion KdV Equation on the Half-Line

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posted on 2020-04-20, 00:00 authored by Fangchi Yan

The initial-boundary value problem (ibvp) for the m-th order Korteweg-de Vries (KdVm) equation on the half-line 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 KdVm, 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.

History

Date Modified

2020-05-25

Defense Date

2020-03-19

CIP Code

  • 27.0101

Research Director(s)

A. Alexandrou Himonas

Degree

  • Doctor of Philosophy

Degree Level

  • Doctoral Dissertation

Alternate Identifier

1155056746

Library Record

5503674

OCLC Number

1155056746

Program Name

  • Mathematics

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