The Null Condition and Global Existence of Nonlinear Elastic Waves
Within the framework of nonlinear hyperelasticity, it is shown that a special class of materials have stored energy functions which give rise to nonlinearities which satisfy a null condition. Under this assumption, the initial value problem for the displacement from equilibrium will be studied. It will be shown that the resulting nonlinear hyperbolic system has global small amplitude classical solutions. The proof combines generalized energy methods with a new decay estimate for the linear problem.
Refreshments will be served at 3:30 PM in Math 401N.