Homogeneous weakly hyperbolic equations with time dependent analytic coefficients
Homogeneous weakly hyperbolic equations with time dependent analytic coefficients
复制标题
具有与时间相关的解析系数的齐次弱双曲方程
DOI：
10.1016/j.jde.2011.04.009
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发表时间：
2011
影响因子：
2.4
通讯作者：
G. Taglialatela
中科院分区：
文献类型：
--
作者：
E. Jannelli;G. Taglialatela
本文讨论解析系数随时间变化的齐次弱双曲型方程的柯西问题。给出了C-∞适定的一个充分条件，当空间维度等于1时，C-适定也是必要条件。本文的主要观点在于只用算子的系数来表示我们的条件，而不需要知道特征根的行为。这是通过使用伴随双曲矩阵的所谓标准对称器来实现的。
This paper concerns the Cauchy problem for homogeneous weakly hyperbolic equations with time depending analytic coefficients. We give a sufficient condition for the C∞-well-posedness which is also necessary if the space dimension is equal to one. The main point of the paper consists in expressing our condition only in terms of the coefficients of the operator, without needing to know the behavior of the characteristic roots. This is made possible by using the so-called standard symmetrizer of a companion hyperbolic matrix.