On the unique continuation property for a nonlinear dispersive system

A. Kozakevicius, Universidade Federal de Santa Maria, Santa Maria, Brasil
O. Vera, Universidad del Bío-Bío, Concepción, Chile

E. J. Qualitative Theory of Diff. Equ., No. 14. (2005), pp. 1-23.

Abstract: We solve the following problem: If $(u,\,v)=(u(x,\,t),\,v(x,\,t))$ is a solution of the Dispersive Coupled System with $t_{1}<t_{2}$ which are sufficiently smooth and such that:
$\,\mbox{supp}\;u(\,.\,,\,t_{j})\subset (a,\,b)\,$
and
$\,\mbox{supp}\;v(\,.\,,\, t_{j})\subset (a,\,b),\,-\,\infty<a<b<\infty ,\,$ $j=1,\,2.\,$
Then $u\equiv 0$ and $v\equiv 0.$

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