Unique continuation for some nonlinear dispersive models

ABSTRACT :

This talk is concerned with unique continuation properties (UCP) for
solutions to some time evolution equations. We shall study two types of
UCP (1) local and (2) asymptotic at infinity.
Roughly, (1) local means : If u, v are solutions of the equation which
agree in an open set D, then they are identical in the whole domain of
definition.
Roughly, (2) asymptotic at infinity means if u, v are solutions such that
||| u(t)-v(t)|||<\Infty for t=t_1,and t=t_2, then they are identical
in the whole domain of definition.
The class of dispersive model to be considered includes the Benjamin-Ono
equation and the Camassa-Holm equation.

Posted on Jul 22, 2019 in Differential Equations, Seminars