Problems involving the evolution of two- and three-dimensional domains arise in many areas of science and engineering. Emphasizing an Eulerian approach, Moving Shape Analysis and Control: Applications to Fluid Structure Interactions presents valuable tools for the mathematical analysis of evolving domains.
The book illustrates the efficiency of the tools presented through different examples connected to the analysis of noncylindrical partial differential equations (PDEs), such as Navier–Stokes equations for incompressible fluids in moving domains. The authors first provide all of the details of existence and uniqueness of the flow in both strong and weak cases. After establishing several important principles and methods, they devote several chapters to demonstrating Eulerian evolution and derivation tools for the control of systems involving fluids and solids. The book concludes with the boundary control of fluid–structure interaction systems, followed by helpful appendices that review some of the advanced mathematics used throughout the text.
This authoritative resource supplies the computational tools needed to optimize PDEs and investigate the control of complex systems involving a moving boundary.
Introduction. An Introductory Example: The Inverse Stefan Problem. Weak Evolution of Sets and Tube Derivatives. Shape Differential Equation and Level Set Formulation. Dynamical Shape Control of the Navier–Stokes Equations. Tube Derivative in a Lagrangian Setting. Sensitivity Analysis for a Simple Fluid–Solid Interaction System. Sensitivity Analysis for a General Fluid–Structure Interaction System. Appendix A: Functional Spaces and Regularity of Domains. Appendix B: Distribution Spaces. Appendix C: The Fourier Transform. Appendix D: Sobolev Spaces. References. Index.