The mixed initial-boundary value problem for reducible quasilinear hyperbolic systems with linearly degenerate characteristics (Q1863455)
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scientific article; zbMATH DE number 1879968
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The mixed initial-boundary value problem for reducible quasilinear hyperbolic systems with linearly degenerate characteristics |
scientific article; zbMATH DE number 1879968 |
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The mixed initial-boundary value problem for reducible quasilinear hyperbolic systems with linearly degenerate characteristics (English)
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11 March 2003
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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.
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linearly degenerate system
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formation of singularity
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nonlinear boundary conditions
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nonlinear hyperbolic waves
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