Boundary Layers for Viscous Perturbations of Noncharacteristic Quasilinear Hyperbolic Problems

In this paper, we study viscous perturbations of quasilinear hyperbolic systems in several dimensions as the viscosity goes to zero. The boundary is noncharacteristic for the hyperbolic system. We in particular describe the boundary layer which arises near the boundary and give a sufficient condition for the convergence of the solution to the solution of some mixed hyperbolic problem with some nonlinear maximal dissipative boundary conditions. A counterexample is given when this condition is not satisfied, and the solution blows up as the viscosity goes to 0.