On a distributed control problem for a coupled chemotaxis-fluid model
type: Item
instance of: scholarly article
title: On a distributed control problem for a coupled chemotaxis-fluid model
zbMATH Open document ID: 1433.35430
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2018-09-06T00:00:00Z
review text: A distributed optimal control problem from chemotaxis is studied. The governing equations are the stationary Patlak-Keller-Segel model and the Navier-Stokes equation for incompressible fluids; the objective involves tracking terms and a Hilbert space regularization. In effect, the system is controlled through a distributed force and a coefficient of chemotactic sensitivity, and the aim is to drive the chemical concentration, the cell density, and the velocity field towards prescribed targets. It is proved that the optimal control problem has an optimal solution. Furthermore, first order optimality conditions are derived.
reviewed by: Florian Mannel
Mathematics Subject Classification ID: 35Q92
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 76D03
Mathematics Subject Classification ID: 92C17
Mathematics Subject Classification ID: 35Q93
Mathematics Subject Classification ID: 93C20
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 6932753
zbMATH Keywords: chemotaxis
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: Patlak-Keller-Segel model
zbMATH Keywords: distributed control
author: María Ángeles Rodríguez-Bellido
author: Diego Armando Rueda-Gómez
author: Elder J. Villamizar-Roa
MaRDI profile type: Publication
full work available at URL: dcdsb.2017208
OpenAlex ID: W2755185705
cites work: Some optimal control problems of multistate equations appearing in fluid mechanics
cites work: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
cites work: Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues
cites work: Su un problema al contorno relativo al sistema di equazioni di Stokes
cites work: MATHEMATICAL MODELLING OF CANCER CELL INVASION OF TISSUE: THE ROLE OF THE UROKINASE PLASMINOGEN ACTIVATION SYSTEM
cites work: Q4275296
cites work: A uniform controllability result for the Keller–Segel system
cites work: A controllability result for a chemotaxis-fluid model
cites work: Collapsing steady states of the Keller–Segel system
cites work: Singular limits in thermodynamics of viscous fluids
cites work: Chemotaxis-fluid coupled model for swimming bacteria with nonlinear diffusion: global existence and asymptotic behavior
cites work: Elliptic partial differential equations of second order
cites work: Boundary Velocity Control of Incompressible Flow with an Application to Viscous Drag Reduction
cites work: A user's guide to PDE models for chemotaxis
cites work: Optimal boundary control of steady-state flow of a viscous inhomogeneous incompressible fluid
cites work: On convergence to equilibria for a chemotaxis model with volume-filling effect
cites work: Q4703032
cites work: Initiation of slime mold aggregation viewed as an instability
cites work: Model for chemotaxis
cites work: A Chemotaxis Model with Threshold Density and Degenerate Diffusion
cites work: Analysis of Neumann Boundary Optimal Control Problems for the Stationary Boussinesq Equations Including Solid Media
cites work: Large amplitude stationary solutions to a chemotaxis system
cites work: A coupled chemotaxis-fluid model: global existence
cites work: A boundary control problem for micropolar fluids
cites work: Mathematical modeling of tumor-induced angiogenesis
cites work: Q3431982
cites work: Steady states with unbounded mass of the Keller–Segel system
cites work: Metastability in chemotaxis models
cites work: Q5533735
cites work: Stationary Solutions of Chemotaxis Systems
cites work: Global existence and boundedness in a Keller-Segel-Stokes model with arbitrary porous medium diffusion
cites work: Overview of mathematical approaches used to model bacterial chemotaxis. II: Bacterial popu\-lations
cites work: Model and analysis of chemotactic bacterial patterns in a liquid medium
cites work: Global Large-Data Solutions in a Chemotaxis-(Navier–)Stokes System Modeling Cellular Swimming in Fluid Drops
cites work: Existence and decay of global smooth solutions to the coupled chemotaxis-fluid model
DOI: 10.3934/DCDSB.2017208
description: scientific article; zbMATH DE number 6932753