= Lax shock admissibility conditions
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For a strictly hyperbolic <system of conservation laws> $U_t+F(U)_x=0$ with ordered <characteristic speeds> $\lambda_1<\cdots<\lambda_n$, a Lax family-$j$ shock has $\lambda_j(U_R)<s<\lambda_j(U_L)$. The remaining families must stay on the same side of $s$: $\lambda_{j-1}(U_L)<s$ and $s<\lambda_{j+1}(U_R)$ where those neighbors exist. These inequalities imply that the lower families have speed below $s$ on both sides and the higher families speed above $s$ on both sides. There are $n+1$ incoming characteristic directions: two from the compressed family and one from each other family. The <Rankine-Hugoniot conditions> supply the jump balance, while these inequalities supply admissibility. For a convex scalar flux this reduces to the <entropy shock> condition.
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