Exact controllability to nonnegative trajectory for a chemotaxis system
Qiang Tao, Muming Zhang
TL;DR
This paper establishes the exact controllability of a chemotaxis system with singular sensitivity using a novel Carleman estimate, and discusses the global existence of nonnegative solutions.
Contribution
It introduces a new global Carleman estimate for coupled parabolic equations with convective terms, enabling controllability results for chemotaxis models.
Findings
Proved controllability of the chemotaxis system.
Established global existence of nonnegative solutions.
Developed a new Carleman estimate for coupled parabolic equations.
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.
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Taxonomy
TopicsMathematical Biology Tumor Growth · Gene Regulatory Network Analysis · Mathematical and Theoretical Epidemiology and Ecology Models