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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Main Author: Mahendra Panthee
Format: Article
Language:English
Published: Texas State University 2005-06-01
Series:Electronic Journal of Differential Equations
Subjects:
Online Access:http://ejde.math.txstate.edu/Volumes/2005/59/abstr.html
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spelling 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
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