\(L^\infty\)-stability of continuous shock waves in a radiating gas model (Q2878994)
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scientific article; zbMATH DE number 6340706
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(L^\infty\)-stability of continuous shock waves in a radiating gas model |
scientific article; zbMATH DE number 6340706 |
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5 September 2014
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hyperbolic-elliptic system
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collision of discontinuities
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\(L^\infty\)-stability of continuous shock waves in a radiating gas model (English)
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The author considers the initial-value problem of the simplified system of radiating gases with one spatial variable. The initial distribution has finite limits in \(\pm\infty\). Exitence of a local solution is established. The difference \(\delta_S\) between values of velocity in \(\pm\infty\) is called shock strength. Stability of shock waves and traveling wave solutions is studied. All subcritical shocks (with \(\delta_S<\sqrt{2}\)) are proven to be stable to small piecewise smooth perturbations, while the critical shock can blow up in finite time.
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