ALMOST GLOBAL EXISTENCE OF DIRICHLET INITIAL-BOUNDARY VALUE PROBLEM FOR NONLINEAR ELASTODYNAMIC SYSTEM OUTSIDE A STAR-SHAPED DOMAIN

This paper deals with the mixed initial-boundary value problem of Dirichlet type for the nonlinear elastodynamic system outside a star-shaped domain. The almost global existence of solution with small initial data to this problem is proved and a lower bound for the lifespan of solutions is given.