Abstract
AbstractWe 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 L1 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 L1 stability of scalar solutions and decay in total variation of the wave speed.
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