ABSTRACT
This chapter presents some recent results in the theory of boundary layers in viscous perturbations of nonlinear hyperbolic systems near a boundary. It discusses the semilinear case and includes the case where the boundary is characteristic for the hyperbolic operator. The chapter is devoted to the case of quasilinear hyperbolic systems, when the boundary is not characteristic. The characteristic case is the case where the matrix has a nontrivial kernel. A very difficult problem is the case of the vanishing viscosity for the Navier-Stokes equations, for which the formal limit is the Euler system with the natural slip condition at the boundary, which is a characteristic quasilinear hyperbolic mixed problem.
