Parameter identification for weakly damped shallow arches

The paper considers shallow arches under weak damping with hinged and clamped boundary conditions. A self-contained presentation of the existence, uniqueness, and regularity of the solutions is provided. The solutions are shown to be continuously dependent on the governing parameters. Furthermore, the solutions are shown to be weakly Gâteaux differentiable. The characterization of the weak Gâteaux derivative is established by introducing the notion of the weakened solution. Such solutions extend the class of weak solutions utilizing J. Lions’ Method of Transposition. rameter identification problem is stated in terms of the best fit to data objective function. This function is shown to be Fréchet differentiable in the interior of the admissible set. The optimal parameters are characterized by a bang–bang control principle.