The generalized Korteweg-de Vries equation on the half line

2001/11/28 by J. E. Colliander, Colliander, J. E., C. E. Kenig +1 · 2 citations
Mathematics · #35Q53 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35Q53

paper · pdf · doi:10.48550/arxiv.math/0111294

added references, fixed typos

arxiv created 2002/03/14 · arxiv updated 2009/11/30

Abstract

The initial-boundary value problem for the generalized Korteweg-de Vries equation on a half-line is studied by adapting the initial value techniques developed by Kenig, Ponce and Vega and Bourgain to the initial-boundary setting. The approach consists of replacing the initial-boundary problem by a forced initial value problem. The forcing is selected to satisfy the boundary condition by inverting a Riemann-Liouville fractional integral.

Cited by

• On the Propagation of Regularity of Solutions to the KdV Equation on the positive Half-line
• The Kawahara equation on star graphs

Related

• The initial-boundary value problem for the Korteweg-de Vries equation
• The initial-boundary value problem for Schrödinger-Korteweg-de Vries system on the half-line
• Regular Global Solutions for A Generalized KdV Equation Posed on A\n Half-Line
• On the Propagation of Regularity of Solutions to the KdV Equation on the positive Half-line
• The KdV equation on the half-line: The Dirichlet to Neumann map