On the Self-similar Zero-viscosity Limit for a Boundary Riemann Problem

Note that the Cauchy and the Dirichlet datum are both constant vectors: we explain why it is meaningful considering this class of problems later on in the introduction. The self-similar viscous approximation (1.1) of an initial-boundary value problem was considered in Joseph and LeFloch [17]: they established compactness of the family Uε and provided an accurate description of a limit. Here we focus on the limit characterization: the main novelty is that we rely on techniques different from those in [17], exploiting an approach based on the analysis of invariant manifolds for ODEs, in the same spirit as in Bianchini and Bressan [4] and Ancona and Bianchini [2]. As a byproduct, our analysis applies directly to non conservative systems ∂tUε +A(Uε)∂xUε = εt ∂ 2 xxUε, (1.3)