  This paper studies the quantitative unique continuation for a semi-linear
parabolic-elliptic coupled system on a bounded domain. This system is a
simplified version of the chemotaxis model introduced by Keller and Segel. With
the aid of priori L^infty-estimates (for solutions of the system) built up in
this paper, we treat the semi-linear parabolic equation in the system as a
linear parabolic equation, and then use the frequency function method and the
localization technique to build up two unique continuation inequalities for the
system. As a consequence of the above-mentioned two inequalities, we have the
following qualitative unique continuation property: if one component of a
solution vanishes in a nonempty open subset at some time T>0, then the solution
is identically zero.
