The mixed initial-boundary value problem for reducible quasilinear hyperbolic systems with linearly degenerate characteristics Original Research Article

In this paper, we prove that the C0 boundedness of solution implies the global existence and uniqueness of C1 solution to the mixed initial-boundary value problem for linearly degenerate, reducible quasilinear hyperbolic systems with nonlinear boundary conditions and we show by an example that the C0 norm of solution may blow up in a finite time. This gives the mechanism of the formation of singularities caused by the interaction of boundary conditions with nonlinear hyperbolic waves. The same result is still valid for the quasilinear hyperbolic system of rich type.