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We prove the uniqueness of solutions to the Dafermos regularization viscouswave fan profiles for Riemann solutions of scalar hyperbolic conservation laws.We emphasize that our results are not restricted to the small self-similarviscosity regime. We rely on suitable adaptations of Serrin's sweepingprinciple and the sliding method from the qualitative theory of semilinearelliptic PDEs. In order to illustrate the delicacy of our result, we prove theexistence of an unbounded solution in the case of Burgers equation. Lastly, wecan combine aspects of these results in order to give a precise description ofthe Dafermos regularization of rarefaction waves of Burgers equation.

Uniqueness for the Dafermos regularization viscous wave fan profiles for Riemann solutions of scalar hyperbolic conservation laws