Moving Shape Analysis and Control illustrates the efficiency of the tools presented through different examples connected to the analysis of noncylindrical partial differential equations, such as the Navier-Stokes equations for incompressible fluids in moving domains.

Features:

• Provides various tools to handle moving domains on the level of intrinsic definition, computation, optimization, and control
• Addresses real-world engineering problems with applications
• Emphasizes the Eulerian approach using evolution and derivation tools for controlling fluids and systems
• Includes two chapters devoted to fluid control described using Navier-Stokes equations
• Features new approaches to deal with boundary control fluid-structure interaction systems

Contents

Introduction

• Classical and Moving Shape Analysis
• Fluid-Structure Interaction Problems
• Plan of the Book
• Detailed Overview of the Book

An Introductory Example: The Inverse Stefan Problem

• The Mechanical and Mathematical Settings
• The Inverse Problem Setting
• The Eulerian Derivative and the Transverse Field
• The Eulerian Material Derivative of the State
• The Eulerian Partial Derivative of the State
• The Adjoint State and the Adjoint Transverse Field

Weak Evolution of Sets and Tube Derivatives

• Weak Convection of Characteristic Functions
• Tube Evolution in the Context of Optimization Problems
• Tube Derivative Concepts
• A First Example: Optimal Trajectory Problem

Shape Differential Equation and level Set Formulation

• Classical Shape Differential Equation Setting
• The Shape Control Problem
• The Asymptotic Behavior
• Shape Differential Equation for the Laplace Equation
• Shape Differential Equation in Rd+1
• The Level Set Formulation

Dynamical Shape Control of the Navier-Stokes Equations

• Elements of Non-Cylindrical Shape Calculus
• Elements of Tangential Calculus
• State Derivative Strategy
• Min-Max and Function Space Parameterization
• Min-Max and Function Space Embedding

Tube Derivative in a Lagrangian Setting

• Evolution Maps
• Navier-Stokes Equations in Moving Domain

Sensivity Analysis for a Simple Fluid Solid Interaction System

• Mathematical Settings
• Well-Posedness of the Coupled System
• Inverse Problem Settings
• KKT Optimality Conditions

Sensitivity Analysis for a General Fluid Structure Interaction System

• Mechanical Problem and Main Result
• KKT Optimality Conditions

Index

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