Slot nozzle design with specified pressure in a given subregion by using embedding method

In this paper we study a shape optimization problem connected with controlled pressure in a subregion of a 2D slot nozzle. Feasible shapes for this problem are characterized only with upper walls. This enables us to seek for the optimum in a class of functions and their derivatives instead of a class of shapes. The shape optimization problem can be written as an optimal control problem, then the resulting distributed control problem is expressed in a measure theoretical form, in fact an infinite dimensional linear programming problem. The optimal measure representing optimal shape is approximated by the solution of a finite dimensional linear programming problem. A brief sensitivity analysis on model parameters is given.