BOUNDARY-LAYERS FOR VISCOUS PERTURBATIONS OF NONCHARACTERISTIC QUASI-LINEAR HYPERBOLIC PROBLEMS

In this paper, we study viscous perturbations of quasilinear hyperboli c systems in several dimensions as the viscosity goes to zero. The bou ndary is noncharacteristic for the hyperbolic system. We in particular describe the boundary layer which arises near the boundary and give a sufficient condition far the convergence of the solution to the solut ion of some mixed hyperbolic problem with some nonlinear maximal dissi pative boundary conditions. A counterexample is given when this condit ion is not satisfied, and the solution blows up as the viscosity goes to 0. (C) 1998 Academic Press.