I am interested in the mathematical control and numerical analysis of those coupled partial differential equations (PDE's) which model the control design of interactive structures as they appear in nature, science, and engineering. By coupled PDE's, we mean those systems which comprise a coupling of two or more disparate dynamics; e.g., a (parabolic) fluid equations coupled to a (hyperbolic) structural equation. Physical systems which can be modeled by such classes of PDE's include structural, structural acoustic, thermal/structure and fluid/structure interaction systems. The consideration of control theory for these coupled PDE's leads to many interesting problems, owning to (i) the pointwise-distributed (and unbounded) nature of the actuators and sensors which are embedded within the structure; (ii) The intrinsic nature of the coupling between the PDE dynamics. The analysis and resolution of control problems involving these coupled models often require varied techniques, such as PDE methods, variational approaches, pseudodifferential/microlocal analysis; etc.
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