Electron. J. Diff. Equ., Vol. 2015 (2015), No. 60, pp. 1-20.

2D Zakharov-Kuznetsov-Burgers equations with variable dissipation on a strip

Nikolai A. Larkin

An initial-boundary value problem for a 2D Zakharov-Kuznetsov-Burgers type equation with dissipation located in a neighborhood of $x=-\infty$ and posed on a channel-type strip was considered. The existence and uniqueness results for regular and weak solutions in weighted spaces as well as exponential decay of small solutions without restrictions on the width of a strip were proven both for regular solutions in an elevated norm and for weak solutions in the $L^2$-norm.

Submitted November 12, 2014. Published March 10, 2015.
Math Subject Classifications: 35Q53, 35B35.
Key Words: KdV-Burgers equation; dispersive equations; exponential decay.

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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

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