Diagonal symmetrizers for hyperbolic operators with triple characteristics
Diagonal symmetrizers for hyperbolic operators with triple characteristics
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DOI：
10.1007/s00208-021-02153-2
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发表时间：
2021-02-06
影响因子：
1.4
通讯作者：
Nishitani, Tatsuo
中科院分区：
文献类型：
--
作者：
Nishitani, Tatsuo
通过对角化主符号及其导数的Bezoutian矩阵，得到了双曲算子的对称化子。这样的对角对称化子被应用到具有三重特征的双曲算子的柯西问题。特别地，证明了关于强双曲算子具有三重有效双曲特征的Ivrii猜想，该猜想适用于系数依赖于时间的微分算子，也适用于具有两个解析系数的自变量的三阶微分算子.
Symmetrizers for hyperbolic operators are obtained by diagonalizing the Bezoutian matrix of the principal symbols and its derivatives. Such diagonal symmetrizers are applied to the Cauchy problem for hyperbolic operators with triple characteristics. In particular, the Ivrii's conjecture concerned with strongly hyperbolic operators with triple effectively hyperbolic characteristics is proved for differential operators with time dependent coefficients, also for third order differential operators with two independent variables with analytic coefficients.