On a distributed control problem for a coupled chemotaxis-fluid model

DOI10.3934/dcdsb.2017208zbMath1433.35430OpenAlexW2755185705MaRDI QIDQ1671046

Maria Angeles Rodríguez-Bellido, Elder Jesús Villamizar-Roa, Diego Armando Rueda-Gómez

Publication date: 6 September 2018

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2017208

zbMATH Keywords

Navier-Stokes equationschemotaxisdistributed controlPatlak-Keller-Segel model

Mathematics Subject Classification ID

Control/observation systems governed by partial differential equations (93C20) Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations for incompressible viscous fluids (76D05) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Existence theories for optimal control problems involving partial differential equations (49J20) Cell movement (chemotaxis, etc.) (92C17) PDEs in connection with control and optimization (35Q93)

Related Items

On a bi-dimensional chemo-repulsion model with nonlinear production and a related optimal control problem, Bilinear optimal control of the Keller-Segel logistic model in \(2D\)-domains, Optimal bilinear control problem related to a chemo-repulsion system in 2D domains, Stationary solutions to a chemo-repulsion system and a related optimal bilinear control problem, An optimal control problem for a Lotka-Volterra competition model with chemo-repulsion, Optimal boundary control for the stationary Boussinesq equations with variable density, A Regularity Criterion for a 3D Chemo-Repulsion System and Its Application to a Bilinear Optimal Control Problem, A 2D model for heat transport in a Hele-Shaw geometry, Bilinear optimal control problem for the stationary Navier-Stokes equations with variable density and slip boundary condition, Unnamed Item, An optimal control problem related to a 3D-chemotaxis-Navier-Stokes model, An optimal control problem for the steady nonhomogeneous asymmetric fluids

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A boundary control problem for micropolar fluids
• Global existence and boundedness in a Keller-Segel-Stokes model with arbitrary porous medium diffusion
• A controllability result for a chemotaxis-fluid model
• A coupled chemotaxis-fluid model: global existence
• Chemotaxis-fluid coupled model for swimming bacteria with nonlinear diffusion: global existence and asymptotic behavior
• Initiation of slime mold aggregation viewed as an instability
• Model for chemotaxis
• Existence and decay of global smooth solutions to the coupled chemotaxis-fluid model
• A user's guide to PDE models for chemotaxis
• Large amplitude stationary solutions to a chemotaxis system
• Model and analysis of chemotactic bacterial patterns in a liquid medium
• Elliptic partial differential equations of second order
• Mathematical modeling of tumor-induced angiogenesis
• Overview of mathematical approaches used to model bacterial chemotaxis. II: Bacterial popu\-lations
• Metastability in chemotaxis models
• Su un problema al contorno relativo al sistema di equazioni di Stokes
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• A Chemotaxis Model with Threshold Density and Degenerate Diffusion
• Collapsing steady states of the Keller–Segel system
• Stationary Solutions of Chemotaxis Systems
• Boundary Velocity Control of Incompressible Flow with an Application to Viscous Drag Reduction
• Some optimal control problems of multistate equations appearing in fluid mechanics
• Analysis of Neumann Boundary Optimal Control Problems for the Stationary Boussinesq Equations Including Solid Media
• Steady states with unbounded mass of the Keller–Segel system
• A uniform controllability result for the Keller–Segel system
• Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues
• Global Large-Data Solutions in a Chemotaxis-(Navier–)Stokes System Modeling Cellular Swimming in Fluid Drops
• MATHEMATICAL MODELLING OF CANCER CELL INVASION OF TISSUE: THE ROLE OF THE UROKINASE PLASMINOGEN ACTIVATION SYSTEM
• On convergence to equilibria for a chemotaxis model with volume-filling effect
• Singular limits in thermodynamics of viscous fluids
• Optimal boundary control of steady-state flow of a viscous inhomogeneous incompressible fluid