The mixed initial-boundary value problem for reducible quasilinear hyperbolic systems with linearly degenerate characteristics
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.
scientific article; zbMATH DE number 1879968