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.
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