Unique continuation property for the Kadomtsev-Petviashvili (KP-II) equation
We generalize a method introduced by Bourgain in cite{Borg} based on complex analysis to address two spatial dimensional models and prove that if a sufficiently smooth solution to the initial value problem associated with the Kadomtsev-Petviashvili (KP-II) equation $$ (u_t+u_{xxx}+uu_{x})_{x} +u_{y...
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Texas State University
2005-06-01
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Online Access: | http://ejde.math.txstate.edu/Volumes/2005/59/abstr.html |
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doaj-5659bdbf2cb348e58f7ce366b851b2422020-11-24T22:47:38ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912005-06-01200559112Unique continuation property for the Kadomtsev-Petviashvili (KP-II) equationMahendra PantheeWe generalize a method introduced by Bourgain in cite{Borg} based on complex analysis to address two spatial dimensional models and prove that if a sufficiently smooth solution to the initial value problem associated with the Kadomtsev-Petviashvili (KP-II) equation $$ (u_t+u_{xxx}+uu_{x})_{x} +u_{yy}=0, quad (x, y) in mathbb{R}^2, ;tinmathbb{R}, $$ is supported compactly in a nontrivial time interval then it vanishes identically.http://ejde.math.txstate.edu/Volumes/2005/59/abstr.htmlDispersive equationsKP equationunique continuation propertysmooth solutioncompact support. |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Mahendra Panthee |
spellingShingle |
Mahendra Panthee Unique continuation property for the Kadomtsev-Petviashvili (KP-II) equation Electronic Journal of Differential Equations Dispersive equations KP equation unique continuation property smooth solution compact support. |
author_facet |
Mahendra Panthee |
author_sort |
Mahendra Panthee |
title |
Unique continuation property for the Kadomtsev-Petviashvili (KP-II) equation |
title_short |
Unique continuation property for the Kadomtsev-Petviashvili (KP-II) equation |
title_full |
Unique continuation property for the Kadomtsev-Petviashvili (KP-II) equation |
title_fullStr |
Unique continuation property for the Kadomtsev-Petviashvili (KP-II) equation |
title_full_unstemmed |
Unique continuation property for the Kadomtsev-Petviashvili (KP-II) equation |
title_sort |
unique continuation property for the kadomtsev-petviashvili (kp-ii) equation |
publisher |
Texas State University |
series |
Electronic Journal of Differential Equations |
issn |
1072-6691 |
publishDate |
2005-06-01 |
description |
We generalize a method introduced by Bourgain in cite{Borg} based on complex analysis to address two spatial dimensional models and prove that if a sufficiently smooth solution to the initial value problem associated with the Kadomtsev-Petviashvili (KP-II) equation $$ (u_t+u_{xxx}+uu_{x})_{x} +u_{yy}=0, quad (x, y) in mathbb{R}^2, ;tinmathbb{R}, $$ is supported compactly in a nontrivial time interval then it vanishes identically. |
topic |
Dispersive equations KP equation unique continuation property smooth solution compact support. |
url |
http://ejde.math.txstate.edu/Volumes/2005/59/abstr.html |
work_keys_str_mv |
AT mahendrapanthee uniquecontinuationpropertyforthekadomtsevpetviashvilikpiiequation |
_version_ |
1725681150179934208 |