Unique continuation inequalities for the parabolic-elliptic chemotaxis system

2021/04/05 by Gengsheng Wang, Wang, Gengsheng, Guojie Zheng +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Numerical methods in inverse problems #Mathematical Biology Tumor Growth

paper · pdf · doi:10.48550/arxiv.2104.01748

Abstract

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 Lⁱnfty-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.

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