Geodesic
Unique continuation property for the Kadomtsev-Petviashvili (KP-II) equation
Electronic Journal of Differential Equations, Tome 2005 (2005).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We generalize a method introduced by Bourgain in citeBorg 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 $$ (u_t+u_{xxx}+uu_{x})_{x} +u_{yy}=0, \quad (x, y) \in \mathbb{R}^2, \;t\in\mathbb{R}, $$ is supported compactly in a nontrivial time interval then it vanishes identically.
Classification : 35Q35, 35Q53
Keywords: dispersive equations, KP equation, unique continuation property, smooth solution, compact support 
@article{EJDE_2005__2005__a219,
     author = {Panthee, Mahendra},
     title = {Unique continuation property for the {Kadomtsev-Petviashvili} {(KP-II)} equation},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2005},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a219/}
}
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Panthee, Mahendra. Unique continuation property for the Kadomtsev-Petviashvili (KP-II) equation. Electronic Journal of Differential Equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a219/