**Cleopatra Christoforou** and **Laura V. Spinolo**

*On the physical and the self-similar viscous approximation of a boundary Riemann problem*

**Pages:** 41-54

**Received:** 14 October 2010

**Accepted:** 24 January 2011

**Mathematics Subject Classification (2010):** 35L65.

**Keywords:**Boundary Riemann problem, viscous approximation, self-similar viscous approximation,
boundary layer, characteristic boundary.

**Abstract:**
We deal with the viscous approximation of a system of conservation laws in one space dimension and
we focus on initial-boundary value problems. It is known that, in general, different viscous approximation
provide different limits because of boundary layer phenomena.
We focus on Riemann-type data and we discuss
a uniqueness criterion for distributional solutions which applies to both the non characteristic and the
boundary characteristic case. As an application, one gets that the limits of the physical viscous
approximation

and of the self-similar viscous approximation

introduced by Dafermos et al. are expected to coincide.

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