Symmetry of \(4\times 4\) strongly hyperbolic operators with characteristic triple point in \(\mathbb{R}^3\) (Q2756135)
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scientific article; zbMATH DE number 1672569
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Symmetry of \(4\times 4\) strongly hyperbolic operators with characteristic triple point in \(\mathbb{R}^3\) |
scientific article; zbMATH DE number 1672569 |
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21 February 2002
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Symmetry of \(4\times 4\) strongly hyperbolic operators with characteristic triple point in \(\mathbb{R}^3\) (English)
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The author considers a first-order \(4\times 4\) system of partial differential operators with constant coefficients in \(\mathbb{R}^3\): NEWLINE\[NEWLINEP=D_t+A_1 D_{x_1} +A_2 D_{x_2}.NEWLINE\]NEWLINE The author assumes \(P\) uniformly diagonalizable; that is equivalent to the strong hyperbolicity of \(P\), according to a result of \textit{K. Kasahara} and \textit{M. Yamaguti} [Mem. Coll. Sci., Univ. Kyoto, Ser. A 33, 1-23 (1960; Zbl 0098.29702)]. Assuming further that the characteristic manifold has a triple point, the author proves pre-symmetry of the matrix-symbol. The proof is obtained by means of a careful study of the possible different canonical forms.
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