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The mixed initial-boundary value problem for reducible quasilinear hyperbolic systems with linearly degenerate characteristics. (English) Zbl 1027.35065

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.

MSC:

35L50 Initial-boundary value problems for first-order hyperbolic systems
35L80 Degenerate hyperbolic equations
35A21 Singularity in context of PDEs
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