A Uniqueness Theorem for a Classical Nonlinear Shallow Shell Model

The main goal of this paper is to establish the uniqueness of solutions of finite energy for a classical dynamic nonlinear thin shallow shell model with clamped boundary conditions. The static representation of the model is an extension of a Koiler shallow shell model. Until now, this has been an open problem in the literature. The primary difficulty is due to a lack of regularity in the nonlinear terms. Indeed the nonlinear terms are not locally Lipshitz with respect to the energy norm. The proof of the theorem relies on sharp PDE estimates that are used to prove uniqueness in a lower topology than the space of finite energy. keywords: Nonlinear shells, weak solutions, uniqueness