Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 40, pp. 1-15.

Title: Well-posedness of  KdV type equations

Authors: Xavier Carvajal  (UFRJ Rio de Janeiro, Brasil)
         Mahendra Panthee (Univ. do Minho, Braga, Portugal)

Abstract:
 In this work, we study the initial value problems associated to some linear
 perturbations of KdV equations. Our focus is in the well-posedness issues
 for initial data given in the L^2-based Sobolev spaces.
 We develop a method that allows us to treat the problem in the Bourgain's space
 associated to the KdV equation. With this method, we can use the multilinear
 estimates developed in the KdV context, thereby getting analogous well-posedness
 results for linearly perturbed equations.

Submitted September 9, 2011. Published March 14, 2012.
Math Subject Classifications: 35A07, 35Q53.
Key Words: Initial value problem; well-posedness; Bourgain spaces,
           KdV equation.