Boundary layers for viscous perturbations of noncharacteristic quasilinear hyperbolic problems. (English) Zbl 0896.35078

The authors study viscous perturbations of quasilinear hyperbolic systems in several dimensions as the viscosity goes to zero. The boundary is noncharacteristic for the hyperbolic system. In particular, they 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 zero.


35L50 Initial-boundary value problems for first-order hyperbolic systems
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
35L60 First-order nonlinear hyperbolic equations
35B25 Singular perturbations in context of PDEs
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