Existence and Uniqueness of Solutions for a Dynamic One-Dimensional Damage Model
Document Type
Article
Publication Date
1-1-1999
Department
Department of Mathematical Sciences
Abstract
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.
Publication Title
Journal of Mathematical Analysis and Applications
Recommended Citation
Frémond, M.,
Kuttler, K.,
&
Shillor, M.
(1999).
Existence and Uniqueness of Solutions for a Dynamic One-Dimensional Damage Model.
Journal of Mathematical Analysis and Applications,
229(1), 271-294.
http://doi.org/10.1006/jmaa.1998.6160
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/3971
