Classification of smooth solutions to 2 x 2 hyperbolic systems with boundary damping

We give a complete classification for breakdown in finite time or global existence of continuously differentiable solutions to hyperbolic systems of two first-order partial differential equations posed on a real bounded interval. with boundary damping and initial data of small magnitude. Structural bounds for the derivatives of the initial data which govern the behavior of the solution are brought to light. We isolate two classes of boundary damping: the strong damping Forbids the solution to blow up after a time that we exhibit while the weak damping permits a late breakdown. The results are applied to nonlinear elasticity. (C) 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.