Exact controllability to nonnegative trajectory for a chemotaxis system

2021/09/06 by Qiang Tao, Tao, Qiang, Muming Zhang +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #FOS: Mathematics #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2109.02305

openalex publication_date 2021/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper studies the controllability for a Keller-Segel type chemotaxis model with singular sensitivity. Based on the Hopf-Cole transformation, a nonlinear parabolic system, which has first-order couplings, and the coupling coefficients are functions that depend on both time and space variables, is derived. Then, the controllability result is proved by a new global Carleman estimate for general coupled parabolic equations allowed to contain a convective term. Also, the global existence of nonnegative solution for the chemotaxis system is discussed.

Citations

• A mathematical model for the roles of pericytes and macrophages in the initiation of angiogenesis. I. The role of protease inhibitors in preventing angiogenesis

Related

• A controllability Result for a Chemotaxis-Fluid Model
• Local Exact Controllability of a Parabolic System of Chemotaxis
• Local Null Controllability of a Chemotaxis System of Parabolic-Elliptic Type
• Global boundedness induced by asymptotically non-degenerate motility in a fully parabolic chemotaxis model with local sensing
• Uniqueness for Keller-Segel-type chemotaxis models