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.

引用

页码：557 / 571

页数：15

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