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September  2008, 10(4): 783-799. doi: 10.3934/dcdsb.2008.10.783

Kawahara equation in a bounded domain

Gleb G. Doronin 1, and  Nikolai A. Larkin 1,

1. 

Departamento de Matemática, Universidade Estadual de Maringá, 87020-900, Maringá, Brazil, Brazil

Received  August 2007 Revised  May 2008 Published  August 2008

This paper deals with an initial-boundary value problem for the nonlinear one-dimensional Kawahara equation posed on a bounded interval. For reasonable initial and boundary conditions we prove the existence and uniqueness of a global regular solution subject to dispersive smoothing. We also show the exponential decay of the obtained solution as $t\to\infty$ and its asymptotics while the coefficient of the higher derivative approaches zero.
Keywords: Nonlinear initial-boundary value problems; odd-order dispersive differential equations; existence and uniqueness..
Mathematics Subject Classification: 35M20, 35Q7.
Citation: Gleb G. Doronin, Nikolai A. Larkin. Kawahara equation in a bounded domain. Discrete and Continuous Dynamical Systems - B, 2008, 10 (4) : 783-799. doi: 10.3934/dcdsb.2008.10.783
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