Electron. J. Diff. Equ., Vol. 2010(2010), No. 168, pp. 1-17.

General mixed problems for the KdV equations on bounded intervals

Nikolai A. Larkin, Jackson Luchesi

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.

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Nikolai A. Larkin
Departamento de Matemática, Universidade Estadual de Maringá
Av. Colombo 5790: Agência UEM, 87020-900, Maringá, PR, Brazil
email: nlarkine@uem.br
Jackson Luchesi
Departamento de Matemática, Universidade Estadual de Maringá
Av. Colombo 5790: Agência UEM, 87020-900, Maringá, PR, Brazil
email: pg44391@uem.br

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