NSF Award
1601127
Research Initiation Awards provide support for junior and mid-career faculty at Historically Black Colleges and Universities who are building new research programs or redirecting and rebuilding existing research programs. It is expected that the award helps to further the faculty member's research capability and effectiveness, improves research and teaching at his home institution, and involves undergraduate students in research experiences. The award to Virginia State University has potential broader impact in a number of areas. The goal of the project is to study the existence and uniqueness of solutions of systems of strongly coupled partial differential equations given an appropriate initial configuration and to study the long time behavior of the solutions. The models have wide applications in areas such as aerospace engineering, civil engineering, and environmental sciences. Undergraduate students will gain research experiences and courses in ordinary and partial differential equations will be enhanced.<br/><br/>The goal of the project is to study the control, optimization and stability analysis centered on physically significant systems composed of dynamical "interactive" inhomogeneous structures, whose behavior is governed by nonlinear systems of coupled partial differential equations (PDEs). The two PDE-components act on separate and adjacent media. Two specific models under consideration are: (1) Fluid-structure interaction (FSI), where the model consists of the Navier Stokes equation coupled on the interface with dynamic elasticity; and (2) Structure acoustic interaction (SAI), in an acoustic chamber with an elastic or thermoelastic shell as a flexible wall. The SAI model consists of hybrid coupling between an acoustic wave equation and a shell equation which is possibly nonlinear. Control theoretic issues to be studied are: (a) stabilization, particularly stabilization of unstable equilibria in FSI and stabilization of SAI subject to weak dissipation; and (b) well-posedness, particularly seeking suitable feedback control such that the solution to FSI with moving interface is well-posed. Both models could be generalized to other structures where the developed mathematical technology could be applied to other coupled systems.
