Weak, classical and intermediate solutions to full von karman system of dynamic nonlinear elasticity

Abstract

Full on Karman suystem describing nonlinear oscilations in dynamic elasticity is considered. The system is equipped with nonlinear boundary conditions prescribing moments and shears subject to a nonlinear, monotone damping. The main result of the paper is the wellposedness theory (existence and uniqueness) for weak, regular and “intermediate” solutions to this problem. in particular, this paper provides an affirmative asnwer to a long-standing open problem in the literature related to the uniqueness of weak (finite energy) solutions in dynamic nonlinear elasticity.

Keywords:

• Full von Karman system
• finite energy solutions uniqueness of weak solutions
• intermediate spaces
• nonlinear damping