ON A DISTRIBUTED CONTROL PROBLEM FOR A COUPLED CHEMOTAXIS-FLUID MODEL

被引：14
|
作者：
Angeles Rodriguez-Bellido, M. [1 ,2 ]
Rueda-Gomez, Diego A. [3 ]
Villamizar-Roa, Elder J. [3 ]
机构：
[1] Univ Seville, Fac Matemat, Dept Ecuac Diferenciales & Anal Numer, C Tarfia S-N, E-41012 Seville, Spain
[2] Univ Seville, IMUS, C Tarfia S-N, E-41012 Seville, Spain
[3] Univ Ind Santander, Escuela Matemat, Bucaramanga 678, Colombia
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2018年 / 23卷 / 02期
关键词：
Chemotaxis; Navier-Stokes equations; Patlak-Keller-Segel model; distributed control; KELLER-SEGEL SYSTEM; STATIONARY SOLUTIONS; GLOBAL EXISTENCE; CONTROLLABILITY RESULT; BOUNDARY CONTROL; STEADY-STATES; DIFFUSION; ANGIOGENESIS; PATTERNS; FLOW;
D O I：
10.3934/dcdsb.2017208
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we analyze an optimal distributed control problem where the state equations are given by a stationary chemotaxis model coupled with the Navier-Stokes equations. We consider that the movement and the interaction of cells are occurring in a smooth bounded domain of R-n; n = 2; 3; subject to homogeneous boundary conditions. We control the system through a distributed force and a coefficient of chemotactic sensitivity, leading the chemical concentration, the cell density, and the velocity field towards a given target concentration, density and velocity, respectively. In addition to the existence of optimal solution, we derive some optimality conditions.
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页码：557 / 571
页数：15
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