Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 168, pp. 1-17.

Title: General mixed problems for the KdV equations on  
       bounded intervals

Authors: Nikolai A. Larkin (Univ. Estadual de Maringa, Brazil)
         Jackson Luchesi   (Univ. Estadual de Maringa, Brazil)

Abstract:
 This article is concerned with initial-boundary value problems
 for the Korteweg-de Vries (KdV) equation on bounded intervals.
 For general linear boundary conditions and small initial data,
 we prove the existence and uniqueness of  global regular solutions
 and its exponential decay, as $t\to\infty$.

Submitted July 23, 2010. Published November 24, 2010.
Math Subject Classifications: 35Q53.
Key Words: KdV equation; global solution; semigroups theory.