Small perturbations of a large shocking simple wave in a strictly hyperbolic 1D conservation law still form a shock, with a universal inverse-cubic leading profile and a Lipschitz maximal development boundary.
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Shock formation in 1D conservation laws I: Inviscid structure
Small perturbations of a large shocking simple wave in a strictly hyperbolic 1D conservation law still form a shock, with a universal inverse-cubic leading profile and a Lipschitz maximal development boundary.