July  2011, 10(4): 1239-1255. doi: 10.3934/cpaa.2011.10.1239

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

1. 

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

Received  February 2010 Revised  October 2010 Published  April 2011

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.

Citation: Pedro Isaza, Jorge Mejía. On the support of solutions to the Kadomtsev-Petviashvili (KP-II) equation. Communications on Pure & Applied Analysis, 2011, 10 (4) : 1239-1255. doi: 10.3934/cpaa.2011.10.1239
References:
[1]

Internat. Math. Res. Notices, 9 (1997), 437-447. doi: 10.1155/S1073792897000305.  Google Scholar

[2]

J. Funct. Anal., 244 (2007), 504-535. doi: 10.1016/j.jfa.2006.11.004.  Google Scholar

[3]

Math. Res. Lett., 15 (2008), 957-971.  Google Scholar

[4]

Inverse Problems, 8 (1992), 673-708. doi: 10.1088/0266-5611/8/5/002.  Google Scholar

[5]

Ann. Inst. H. Poincaré Anal. Non Linéaire, 26 (2009), 917-941. doi: 10.1016/j.anihpc.2008.04.002.  Google Scholar

[6]

Comm. Partial Differential Equations, 26 (2001), 1027-1054. doi: 10.1081/PDE-100002387.  Google Scholar

[7]

Electron. J. Differential Equations, 2003 (2003), 1-12.  Google Scholar

[8]

J. Differential Equations, 247 (2009), 1851-1865. doi: 10.1016/j.jde.2009.03.022.  Google Scholar

[9]

Nonlinear Anal., 72 (2010), 4016-4029. doi: 10.1016/j.na.2010.01.033.  Google Scholar

[10]

Ann. Inst. H. Poincaré Anal. Non linéaire, 19 (2002), 191-208. doi: 10.1016/S0294-1449(01)00073-7.  Google Scholar

[11]

Electron. J. Differential Equations, 2005 (2005), 1-12.  Google Scholar

[12]

Applied Mathematical Sciences, 44, Springer-Verlag, New York, 1983.  Google Scholar

[13]

J. Differential Equations, 66 (1987), 118-139. doi: 10.1016/0022-0396(87)90043-X.  Google Scholar

[14]

Internat. Math. Res. Notices, 2 (2001), 77-114. doi: 10.1155/S1073792801000058.  Google Scholar

show all references

References:
[1]

Internat. Math. Res. Notices, 9 (1997), 437-447. doi: 10.1155/S1073792897000305.  Google Scholar

[2]

J. Funct. Anal., 244 (2007), 504-535. doi: 10.1016/j.jfa.2006.11.004.  Google Scholar

[3]

Math. Res. Lett., 15 (2008), 957-971.  Google Scholar

[4]

Inverse Problems, 8 (1992), 673-708. doi: 10.1088/0266-5611/8/5/002.  Google Scholar

[5]

Ann. Inst. H. Poincaré Anal. Non Linéaire, 26 (2009), 917-941. doi: 10.1016/j.anihpc.2008.04.002.  Google Scholar

[6]

Comm. Partial Differential Equations, 26 (2001), 1027-1054. doi: 10.1081/PDE-100002387.  Google Scholar

[7]

Electron. J. Differential Equations, 2003 (2003), 1-12.  Google Scholar

[8]

J. Differential Equations, 247 (2009), 1851-1865. doi: 10.1016/j.jde.2009.03.022.  Google Scholar

[9]

Nonlinear Anal., 72 (2010), 4016-4029. doi: 10.1016/j.na.2010.01.033.  Google Scholar

[10]

Ann. Inst. H. Poincaré Anal. Non linéaire, 19 (2002), 191-208. doi: 10.1016/S0294-1449(01)00073-7.  Google Scholar

[11]

Electron. J. Differential Equations, 2005 (2005), 1-12.  Google Scholar

[12]

Applied Mathematical Sciences, 44, Springer-Verlag, New York, 1983.  Google Scholar

[13]

J. Differential Equations, 66 (1987), 118-139. doi: 10.1016/0022-0396(87)90043-X.  Google Scholar

[14]

Internat. Math. Res. Notices, 2 (2001), 77-114. doi: 10.1155/S1073792801000058.  Google Scholar

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