Local exact controllability to positive trajectory for parabolic system of chemotaxis
2016
In this paper, we study controllability for a parabolic system of
chemotaxis. With one control only, the local exact controllability to
positive trajectory of the system is obtained by applying Kakutani's fixed
point theorem and the null controllability of associated linearized
parabolic system. The positivity of the state is shown to be remained in the
state space. The control function is shown to be in $L^\infty(Q)$, which is
estimated by using the methods of maximal regularity and $L^p$-$L^q$
estimate for parabolic equations.
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