The Cauchy problem for properly hyperbolic equations in one space variable

被引：3

作者：

Spagnolo, Sergio ^{[1
]}

Taglialatela, Giovanni ^{[2
]}

机构：

[1] Univ Pisa, Dipartimento Matemat, Largo Bruno Pontecorvo 5, I-56127 Pisa, Italy

[2] Univ Bari Aldo Moro, Dipartimento Econ & Finanza, I-70124 Bari, Italy

来源：

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS | 2022年 / 19卷 / 03期

关键词：

Weakly hyperbolic equation; Cauchy problem; symetrizer; SYMMETRIZATION; PROPAGATION; POLYNOMIALS; OPERATORS; SYSTEMS; ROOTS;

D O I：

10.1142/S0219891622500138

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

this paper, we consider the Cauchy problem for higher-order weakly hyperbolic equations assuming that the principal symbol depends only on one space variable and the characteristic roots tau(j) verify an inequality like tau(2)(j) (x) + tau(2 )(k)(x) <= M (tau(j) (x) - tau(k) (x))(2). We prove that the Cauchy problem is well-posed in C-infinity if the operators with frozen coefficients are uniformly hyperbolic in the sense of Garding.

引用

页码：439 / 466

页数：28

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