Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 1. Dynamic Elastic Bar Theory . . . . . . . . . . . . . . . . . . . . . . . 126 2. Existence of Solutions with Phase Boundaries . . . . . . . . . . . . . . . 129 3. Extensions of Theorem 1 . . . . . . . . . . . . . . . . . . . . . . . . . 133 A. Data prescribed on both sides of the phase boundary . . . . . . . . . . . 133 B. Global solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 C. Invariance groups . . . . . . . . . . . . . . . . . . . . . . . . . . 136 4. Interaction of Sound Waves with a Phase Boundary . . . . . . . . . . . . . 136 5. The Riemann Problem and Admissibility . . . . . . . . . . . . . . . . . 143 A. The Riemann problem. Single phase boundary . . . . . . . . . . . . . 143 B. The Riemann problem. Double phase boundary . . . . . . . . . . . . . 147 C. Admissibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 1. Consistency with static stability theory . . . . . . . . . . . . . . . . 150 2. Consistency with viscoelastic bar theory . . . . . . . . . . . . . . . 153 3. Consistency with the maximal rate of decay of entropy . . . . . . . . . 156 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
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