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Shape optimization for stationary Navier-Stokes equations

Halanay A., Tiba D.

Control and Cybernetics

2009

Vol. 38, no 4B

1359-1374

This work discusses geometric optimization problems governed by stationary Navier-Stokes equations. Optimal domains are proved to exist under the assumption that the family of admissible domains is bounded and satisfies the Lipschitz condition with a uniform constant, and in the absence of the uniqueness property for the state system. Through the parametrization of the admissible shapes by continuous functions defined on a larger universal domain, the optimization parameter becomes a control, i.e. an element of that family of continuous functions. The approximating extension technique via the penalization of the Navier-Stokes equation enables the approximation of the associated shape optimization problem by an optimal control problem. Results on existence and uniqueness are proved for the approximating problem and a gradient-type algorithm is indicated.

Stability and accuracy of steady-state motions in loaded copying system : analytical approach

Halanay A., Safta C. A.

Computer Assisted Mechanics and Engineering Sciences

1999

Vol. 6, No. 1

107-136

An analyticalstudy of stability is made for a hydromechanical servomechanism used in copying systems. In the framework of a nonlinear system of ODE mathematically modelling the servomechanism, we prove that for a ramp input the steady-state solution bifurcates into a stable limit cycle for a certain value of the underlap spool valve.