Electron. J. Diff. Eqns., Vol. 2008(2008), No. 127, pp. 1-23.

Well-posed initial-boundary value problems for the Zakharov-Kuznetsov equation

Andrei V. Faminskii

Abstract:
This paper deals with non-homogeneous initial-boundary value problems for the Zakharov-Kuznetsov equation, which is one of the variants of multidimensional generalizations of the Korteweg-de Vries equation. Results on local and global well-posedness are established in a scale of Sobolev-type spaces under natural assumptions on initial and boundary data.

Submitted February 23, 2008. Published September 10, 2008.
Math Subject Classifications: 35Q72.
Key Words: Zakharov-Kuznetsov equation; boundary value problems; well-posedness.

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Andrei V. Faminskii
Department of Mathematics
Peoples' Friendship University of Russia
Miklukho--Maklai str. 6, Moscow, 117198, Russia
email: andrei_faminskii@mail.ru

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