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1996 Local existence in time of solutions to higher-order nonlinear dispersive equations
Nakao Hayashi
Differential Integral Equations 9(5): 879-890 (1996).

Abstract

We study a system of nonlinear dispersive equations of the form $$ \partial_t u_k + \partial_x^{2j+1}u_k + F_k(u_1,\ldots ,u_n,\ldots , \partial_x^{2j}u_1, \ldots , \partial_x^{2j} u_n)=0, (t,x) \in \mathbf{R}\times h{\mathbf{R}}, $$ where $k=1,\ldots ,n$, $j\in \mathbf{N}$ and $F_k(\cdot)$ is a polynomial having no constant or linear terms. Local existence of solutions to the associated initial value problem is shown without a smallness condition on the data.

Citation

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Nakao Hayashi. "Local existence in time of solutions to higher-order nonlinear dispersive equations." Differential Integral Equations 9 (5) 879 - 890, 1996.

Information

Published: 1996
First available in Project Euclid: 6 May 2013

zbMATH: 0849.35129
MathSciNet: MR1392085

Subjects:
Primary: 35G25
Secondary: 35A07 , 35Q30

Rights: Copyright © 1996 Khayyam Publishing, Inc.

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Vol.9 • No. 5 • 1996
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