We study the large time behavior of solutions of the one‐dimensional equations of elasticity, typically a nonconvex system of conservation laws. We show that solutions with compact initial support converge in L 1 to a superposition of N ‐waves, at algebraic rate. Likewise, we show that the perturbation expansion of weakly nonlinear geometric optics is uniformly valid to second order. Our analysis uses approximate scalar laws, together with L 1 stability of scalar solutions and decay in total variation of the wave speed.
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Kevin Zumbrun (1993) studied this question.
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