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November/December 2010 An initial boundary-value problem for the Zakharov-Kuznetsov equation
Jean-Claude Saut, Roger Temam
Adv. Differential Equations 15(11/12): 1001-1031 (November/December 2010).

Abstract

We introduce and study an initial and boundary-value problem for the Zakharov-Kuznetsov equation posed on an infinite strip of ${\mathbb{R}^{d+1}}$, $d=1,2$. After establishing a suitable trace theorem, we first consider the linearized case and define the corresponding semigroup on $L^2$ and prove that it has a global smoothing effect. Then we proceed to the nonlinear case and use the smoothing effect to prove in both dimensions the existence of (unique when $d=1$) global weak solutions of the initial and boundary problem with null boundary conditions and $L^2$ initial data.

Citation

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Jean-Claude Saut. Roger Temam. "An initial boundary-value problem for the Zakharov-Kuznetsov equation." Adv. Differential Equations 15 (11/12) 1001 - 1031, November/December 2010.

Information

Published: November/December 2010
First available in Project Euclid: 18 December 2012

zbMATH: 1219.35253
MathSciNet: MR2743493

Subjects:
Primary: 35A01, 35A02, 35Q53

Rights: Copyright © 2010 Khayyam Publishing, Inc.

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Vol.15 • No. 11/12 • November/December 2010
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