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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