趋化系统的非负轨迹精确可控性

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2025-01-22 DOI:10.1007/s00245-025-10221-1

Qiang Tao, Muming Zhang

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引用次数: 0

摘要

本文研究了一类具有奇异灵敏度的Keller-Segel型趋化性模型的可控性。基于Hopf-Cole变换，导出了一类具有一阶耦合且耦合系数是依赖于时间和空间变量的函数的非线性抛物型系统。然后，用一种新的全局Carleman估计证明了含对流项的一般耦合抛物方程的可控性结果。同时，讨论了趋化系统的非负解的整体存在性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Exact Controllability to Nonnegative Trajectory for a Chemotaxis System

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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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.