Existence of solution in thickness optimization problem for a plate
We consider the optimization of one of the linear parameters of a thin plate subject to dynamic forces. The problem is formulated as an optimal control problem for partial differential equations with phase constraints, and the existence of solution is proved by using the Weierstrass theorem. However, the application of this theorem requires a proof of compactness of the feasible set. Here compactness of the feasible set is proved using continuous dependence of the solution of partial differential equations of fourth order on input values (the coefficients, the right-hand side, and the initial conditions).
continuous dependence of solution on input values
scientific article; zbMATH DE number 1051118
scientific article