Topics in Mathematical Fluid Mechanics and Shape Optimization
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Date
2019-07-08
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Technical university of Liberec
Abstract
This habilitation thesis is based on the author's contributions to the mathematical
theory of incompressible
uids and to the shape optimization in
uid
mechanics. In Chapter 2, an overview of basic equations, theory of weak solutions
and nite-element approximation for incompressible
uids is given.
Chapter 3 is devoted to the formulation of shape optimization problems, to
the questions of existence of solutions, approximation and di erentiability.
Finally, in Chapter 4 some results obtained by the author are mentioned,
namely on the theory of non-Newtonian piezoviscous
uids, applied shape
optimization and sensitivity analysis.