The mixed initial-boundary value problem for reducible quasilinear hyperbolic systems with linearly degenerate characteristics (Q1863455)

It is proved that the \(C^0\) boundedness implies the global existence and uniqueness of \(C^1\) solutions to mixed initial-boundary value problems for linearly degenerate, reducible quasilinear hyperbolic systems with nonlinear boundary conditions. It is shown by an example that the \(C^0\) norm of the solution may blow up in finite time. This gives the mechanism of the formation of singularities caused by the interaction of boundary conditions with nonlinear hyperbolic waves.