Abstract
In this paper, we study controllability for a parabolic system ofchemotaxis. With one control only, the local exact controllability topositive trajectory of the system is obtained by applying Kakutani's fixedpoint theorem and the null controllability of associated linearizedparabolic system. The positivity of the state is shown to be remained in thestate space. The control function is shown to be in $L^\infty(Q)$, which isestimated by using the methods of maximal regularity and $L^p$-$L^q$estimate for parabolic equations.
Highlights
Introduction and main resultsLet Ω ⊂ RN (N ≥ 1) be a bounded domain with sufficiently smooth boundary ∂Ω
The main result of this paper is the following Theorem 1.5
We only show the required estimations with respect to time T
Summary
Introduction and main resultsLet Ω ⊂ RN (N ≥ 1) be a bounded domain with sufficiently smooth boundary ∂Ω. The strict positive solution to Equation (2) is claimed by the following Theorem 1.2.
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