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We deal with initial-boundary value problems for systems of conservation lawsin one space dimension and we focus on the boundary Riemann problem. It isknown that, in general, different viscous approximations provide differentlimits. In this paper, we establish sufficient conditions to conclude that twodifferent approximations lead to the same limit. As an application of thisresult, we show that, under reasonable assumptions, the self-similarsecond-order approximation and the classical viscous approximation provide thesame limit. Our analysis applies to both the characteristic and the noncharacteristic case. We require neither genuine nonlinearity nor lineardegeneracy of the characteristic fields.

A uniqueness criterion for viscous limits of boundary Riemann problems