High frequency waves and the maximal smoothing effect for nonlinear scalar conservation laws (Q2878995)
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scientific article; zbMATH DE number 6340707
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | High frequency waves and the maximal smoothing effect for nonlinear scalar conservation laws |
scientific article; zbMATH DE number 6340707 |
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5 September 2014
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multidimensional conservation laws
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entropy solutions
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nonlinear geometric optics
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High frequency waves and the maximal smoothing effect for nonlinear scalar conservation laws (English)
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The author applies supercritical geometric optics to highlight the maximal regularizing effect for multidimensional scalar conservation laws with smooth nonlinear flux vectors. Namely, a sequence of highly oscillating entropy solutions is constructed, which is bounded in the Sobolev spaces \(W^{s,1}_{\mathrm{loc}}\), \(s\leq\alpha\), where \(\alpha\) is the critical exponent, while this sequence is unbounded in \(W^{s,1}_{\mathrm{loc}}\) for all \(s>\alpha\).
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