= Vanishing viscosity approximation
{title2=$\varepsilon\downarrow0$}
This approximation studies the limit of a <viscous scalar conservation law> as its positive diffusion coefficient tends to zero. Under hypotheses giving compactness and appropriate convergence, the viscous entropy dissipation selects an <entropy solution> of the inviscid <scalar conservation law>. Fixed-phase decreasing <travelling waves> for a strictly convex flux converge to an <entropy shock>. Translating each profile differently can change or destroy the limit, so phase or initial data must specify the family.
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