A Uniqueness Criterion for Viscous Limits of Boundary Riemann Problems

We deal with initial-boundary value problems for systems of conservation laws in one space dimension and we focus on the so-called boundary Riemann problem. It is known that, in general, different viscous approximations provide different limits. We establish sufficient conditions to conclude that two different approximations lead to the same limit. As an application of this result, we show that, under reasonable assumptions, the self-similar second-order approximation ∂tU ε + ∂xF (U ) = ε t ∂x ` B(Uε)∂xU ε ́ and the classical viscous approximation ∂tU ε + ∂xF (U ) = ε∂x ` B(Uε)∂xU ε ́ provide the same limit as ε → 0. Our analysis applies to both the characteristic and non characteristic case.