Existence and Uniqueness of Solutions for a Dynamic One-Dimensional Damage Model

We consider a one-dimensional dynamic model that describes the evolution of damage caused by tension in a viscoelastic material. The process is modeled by a coupled set of two differential inclusions for the elastic displacement and damage fields. We establish the existence of local weak solutions. The existence result is derived from the a priori estimates obtained for a sequence of regularized, truncated, and time-retarded approximations. We also establish the existence of the unique weak solution of a simplified version of the model.