Moving Shape Analysis and Control

Presenting a mathematical analysis of problems related to the evolution of domains, this book provides various tools to handle moving domains on the levels of intrinsic definition, computation, optimization, and control. It addresses real-world engineering problems with applications to free surface flows, and fracture and contact problems.

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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.