Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 127, pp. 1-23.

Title: Well-posed initial-boundary value problems for the
       Zakharov-Kuznetsov equation
  
Author: Andrei V. Faminskii (Peoples' Friendship Univ., Russia)

Abstract:
 This paper deals with non-homogeneous initial-boundary value problems
 for the Zakharov-Kuznetsov equation, which is one of the variants of
 multidimensional generalizations of the Korteweg-de Vries equation.
 Results on local and global well-posedness are established in a scale
 of Sobolev-type spaces under natural assumptions on initial and boundary
 data.
 
Submitted February 23, 2008. Published September 10, 2008.
Math Subject Classifications: 35Q72.
Key Words: Zakharov-Kuznetsov equation; boundary value problems;
           well-posedness.