The residual boundary conditions coming from the real vanishing viscosity method (Q1599881)

The author studies an initial-boundary value problem for the hyperbolic-parabolic system of conservation laws with a small parameter \(u_t+ F(u)_x =\varepsilon(B(u) u_x)_x\). In the noncharacteristic case by using boundary layer analysis he gives a set of boundary conditions, the set of residual boundary conditions \({\mathcal C}\), for the inviscid system. Some geometric property of \({\mathcal C}\) is given. In multidimensional case he shows that the Kreiss-Lopatinski determinant for the hyperbolic system linearized in a constant state in \({\mathcal C}\) is equal to the reduced Evans function for the viscous system linearized in the corresponding profile of boundary layer.