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On the solution of some maximization problems based on a Jensen inequality

Scheiber E., Lupu M.

Demonstratio Mathematica

2004

Vol. 37, nr 3

719--726

Models of fluid mechanics phenomena like the deflector of maximal drag or maximal lifting lead to maximization problems whose solutions are obtained using a method based on a Jensen inequality. The purpose of this paper is to point out the united character of tne given solutions. A scheme is derived for an unconstrained and for a constrained maximization problem, which is applied to four examples.

Optimal airfoil in an inverse problem of jet aerodynamics

Lupu M., Scheiber E.

Computer Assisted Mechanics and Engineering Sciences

2000

Vol. 7, No. 2

227-238

The paper deals with a special inverse boundary problem, when the boundary of the domain is completely unknown and a singular integral equation for the velocity angle is obtained. For the model of free plane symmetric incompressible jet forked by an airfoil, the boundary equations and airfoil shape are ``a posteriori'' determined, while the velocity along them is ``a priori'' prescribed. With the aim to obtain minimum drag, in the present paper there is solved the optimization problem for airfoils, using the penalty method and the golden section method. In the case of optimum, numerical computations are performed and the airfoil design together with the drag coefficient are obtained.

The Dirichlet problem for biharmonic equation in case the half plane

Lupu M.

Demonstratio Mathematica

1999

Vol. 32, nr 1

41-53

Using the representations of the solution of Dirichlet problem for the half plane, the basic biharmonic problem (BP) is solved. Applying the half plane theorem on Almansi type representation of the solution is given by direct or analytical methods. New formulas are proved and for special cases some applications are presented.