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2008 A remark on the Cauchy problem for the generalized Benney-Luke equation
José Raúl Quintero
Differential Integral Equations 21(9-10): 859-890 (2008).

Abstract

In this article, we address the well posedness of the Cauchy problem associated with the generalized Benney--Luke equation in $\mathbb R^{1+2}:$ \begin{multline*} \Phi_{tt} - \Delta \Phi + a \Delta^2 \Phi - b \Delta \Phi_{tt} + \theta\Big ( \Phi_t \big [\partial_{x} \big [ \big (\partial_{x} \Phi \big )^{p} \big ]+ \partial_{y} \big [ \big (\partial_{y}\Phi \big )^{p} \big ] \big ] \\ + 2 \big [ \big (\partial_{x} \Phi \big )^{p}\Phi_{xt}+ \big (\partial_{y} \Phi \big )^{p}\Phi_{yt} \big ] \Big ) + \beta \nabla \cdot \big (|\nabla \Phi|^m \nabla \Phi \big )=0, \end{multline*} under a reasonable ``physical" initial condition, which is imposed from the formal derivation of the Benney-Luke water wave model.

Citation

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José Raúl Quintero. "A remark on the Cauchy problem for the generalized Benney-Luke equation." Differential Integral Equations 21 (9-10) 859 - 890, 2008.

Information

Published: 2008
First available in Project Euclid: 20 December 2012

zbMATH: 1224.35263
MathSciNet: MR2483339

Subjects:
Primary: 35L75
Secondary: 35B30, 35L30, 35Q35, 76B03, 76B15

Rights: Copyright © 2008 Khayyam Publishing, Inc.

JOURNAL ARTICLE
32 PAGES


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Vol.21 • No. 9-10 • 2008
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