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Optimal control problems for the equation of motion of membrane with strong viscosity. (English) Zbl 1101.49016

An equation with strong viscosity term is considered to modelise the vibration of the longitudinal motion of a membrane.

The purpose of this paper is to establish the necessary conditions of optimality for various observation cases. The Gâteaux differentiability of the cost functional is used to obtain the adjoint system. In the velocity observation case, a first order Volterra integro-differential equation is utilised as a proper adjoint system.

MSC:
49K20Optimal control problems with PDE (optimality conditions)
49J50Fréchet and Gateaux differentiability