Electron. J. Diff. Eqns., Vol. 2005(2005), No. 59, pp. 1-12.

Unique continuation property for the Kadomtsev-Petviashvili (KP-II) equation

Mahendra Panthee

Abstract:
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
$$ (u_t+u_{xxx}+uu_{x})_{x} +u_{yy}=0, \quad (x, y) \in \mathbb{R}^2, \;t\in\mathbb{R}, $$
is supported compactly in a nontrivial time interval then it vanishes identically.

Submitted April 9, 2005. Published June 10, 2005.
Math Subject Classifications: 35Q35, 35Q53
Key Words: Dispersive equations; KP equation; unique continuation property; smooth solution; compact support.

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Mahendra Panthee
Central Department of Mathematics
Tribhuvan University, Kirtipur, Kathmandu, Nepal
and Department of Mathematics
CMAGDS, IST, 1049-001
Av. Rovisco Pais, Lisbon, Portugal
email: mpanthee@math.ist.utl.pt

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