Electron. J. Diff. Equ., Vol. 2013 (2013), No. 159, pp. 1-21.

General boundary conditions for the Kawahara equation on bounded intervals

Nikolai A. Larkin, Marcio H. Simoes

This article is concerned with initial boundary value problems for the Kawahara equation on bounded intervals. For general linear boundary conditions and small initial data, we prove the existence and uniqueness of a global regular solution and exponential decay as t approaches infinty.

Submitted February 20, 2013. Published July 11, 2013.
Math Subject Classifications: 35M20, 35Q72.
Key Words: Kawahara equation; global solution; decay of solutions.

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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
Márcio Hiran Simões
Universidade Tecnológica Federal do Paraná
Rua Marcílio Dias
635 - 86812-460, Apucarana, PR, Brazil
email: marcio@utfpr.edu.br

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