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Main Title: Distributed Control for a Class of Non-Newtonian Fluids
Author(s): Slawig, Thomas
Type: Research Paper
Abstract: We consider control problems with a general cost functional where the state equations are the stationary, incompressible Navier-Stokes equations with shear-dependent viscosity. The equations are quasi-linear. The control function is given as the inhomogeneity of the momentum equation. In this paper we study a general class of viscosity functions which correspond to shear-thinning or shear-thickening behavior. The basic results concerning existence, uniqueness, boundedness, and regularity of the solutions of the state equations are reviewed. The main topic of the paper is the proof of Gâteaux differentiability, which extends known results. It is shown that the derivative is the unique solution to a linearized equation. Moreover necessary first order optimality conditions are stated, and the existence of a solution of a class of control problems is shown.
Subject(s): optimal control
non-Newtonian fluids
quasilinear elliptic system
optimality conditions
Issue Date: 1-Sep-2004
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 49J50 Fréchet and Gateaux differentiability
49J20 Optimal control problems involving partial differential equations
76D55 Flow control and optimization
35J60 Nonlinear PDE of elliptic type
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2004, 23
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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