Global well-posedness of two initial-boundary-value problems for the Korteweg-de Vries equation

By Andrei V. Faminskii. Differential and Integral Equations, 2007

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Abstract. Two initial–boundary-value problems for the Korteweg–de Vries equation in a half-strip with two boundary conditions and in abounded rectangle are considered and results on local and global well-posedness of these problems are established in Sobolev spaces of variousorders, including fractional. Initial and boundary data satisfy natural(or close to natural) conditions, originating from properties of solutionsof a corresponding initial-value problem for a linearized KdV equation.An essential part of the study is the investigation of special solutions ofa “boundary potential” type for this linearized KdV equation. 1. IntroductionThe main goal of this paper is to study global well-posedness in fractional-order Sobolev spaces of initial–boundary-value problems for the Korteweg–de Vries equation (KdV) u t + u xxx + au x + uu x = f ( t,x ) (1.1)( u = u ( t,x ), a is an arbitrary real constant) in two domains: a left half-stripΠ −T =(0 ,T ) × R − and a bounded rectangle Q T =(0 ,T )

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/db25683a28bbebd0928d11d97f2da9f9ddba5c76

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In Mathematical Physics

  1. Chaohua Jia
  2. Bingyu Zhang
  3. Andrei V. Faminskii

In Statistical and Nonlinear Physics

  1. Chaohua Jia
  2. Bingyu Zhang

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