Distributed Control for a Class of Non-Newtonian Fluids
| dc.contributor.author | Slawig, Thomas | |
| dc.date.accessioned | 2021-12-17T10:06:00Z | |
| dc.date.available | 2021-12-17T10:06:00Z | |
| dc.date.issued | 2004-09-01 | |
| dc.description.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. | en |
| dc.identifier.issn | 2197-8085 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/15531 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-14304 | |
| dc.language.iso | en | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject.ddc | 510 Mathematik | en |
| dc.subject.other | optimal control | en |
| dc.subject.other | non-Newtonian fluids | en |
| dc.subject.other | quasilinear elliptic system | en |
| dc.subject.other | optimality conditions | en |
| dc.title | Distributed Control for a Class of Non-Newtonian Fluids | en |
| dc.type | Research Paper | en |
| dc.type.version | submittedVersion | en |
| tub.accessrights.dnb | free | en |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | en |
| tub.series.issuenumber | 2004, 23 | en |
| tub.series.name | Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin | en |
| tub.subject.msc2000 | 49J50 Fréchet and Gateaux differentiability | en |
| tub.subject.msc2000 | 49J20 Optimal control problems involving partial differential equations | en |
| tub.subject.msc2000 | 76D55 Flow control and optimization | en |
| tub.subject.msc2000 | 35J60 Nonlinear PDE of elliptic type | en |
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