Existence and uniqueness are established for solutions to the viscous conservation law with positive measure initial data when the flux satisfies a p-condition.
Serre, Stabilite L1 d’ondes progressives de lois de conservation scalaires , Expos´ e VIII in ” ´Equations aux D´ eriv´ ees Partielles”, Ecole Polytechnique 1998-1999
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Viscous Conservation Laws in 1d With Measure Initial Data
Existence and uniqueness are established for solutions to the viscous conservation law with positive measure initial data when the flux satisfies a p-condition.