Unique continuation inequalities for the parabolic-elliptic chemotaxis system

This paper studies the quantitative unique continuation for a semi-linear parabolic-elliptic coupled system on bounded domain Ω. is simplified version of chemotaxis model introduced by Keller and Segel in [14]. With aid priori L∞-estimates (for solutions system) built up this paper, we treat parabolic equation as linear equation, then use frequency function method localization technique to build two inequalities system. As consequence above-mentioned inequalities, have following qualitative property: if one component solution vanishes nonempty open subset ω⊂Ω at some time T>0, identically zero.