On the support of solutions to the Kadomtsev-Petviashvili (KP-II) equation

Pedro Isaza; Jorge Mejía

doi:10.3934/cpaa.2011.10.1239

Article Contents

2011, Volume 10, Issue 4: 1239-1255. Doi: 10.3934/cpaa.2011.10.1239

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On the support of solutions to the Kadomtsev-Petviashvili (KP-II) equation

Pedro Isaza^1, and
Jorge Mejía^1,

1.
Departamento de Matemáticas, Universidad Nacional de Colombia, A. A. 3840 Medellín

Received: January 31, 2010

Revised: September 30, 2010

Published: June 2011

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Abstract

In this article we prove that sufficiently smooth solutions of the Kadomtsev-Petviashvili (KP-II) equation:

$ \partial _t u+\partial^3_x u+\partial^{-1}_x\partial^2_y u+u\partial_x u =0, $

that have compact support for two different times are identically zero.

Keywords:

Nonlinear dispersive equations,
estimates of Carleman type.

Mathematics Subject Classification: Primary: 35Q53; Secondary: 37K05.

Citation:

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References

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