Diierentiability of Solutions of an Electro-elasticity Model W.r.t. Parameters

A model describing a linear thin plate exited by a piezoelectric patch is considered. The peculiarity of this model consists in the presence of an unbounded input operator on the right-hand-side of the model's equation. The main purpose of the paper is to prove the existence of derivatives of solutions with respect to parameters. Such a diierentiability is proved for an appropriate space, which enables us to handle pointwise measurements of data when applying a gradient descent method to the estimation of unknown parameters. It is shown that the derivatives can be computed using well-known variational equations. The paper is illustrated by computer simulations.