Diagonal symmetrizers for hyperbolic operators with triple characteristics

被引：5

作者：

Nishitani, Tatsuo ^{[1
]}

机构：

[1] Osaka Univ, Dept Math, Osaka, Japan

来源：

MATHEMATISCHE ANNALEN | 2022年 / 383卷 / 1-2期

关键词：

Primary; 35L30; Secondary; 35G10; LOCAL ENERGY INTEGRALS; CAUCHY-PROBLEM; WELL-POSEDNESS; EQUATIONS;

D O I：

10.1007/s00208-021-02153-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：529 / 569

页数：41

共 31 条

[1]

[Anonymous], 1973, The theory of partial differential equations

[2] Cauchy problem for effectively hyperbolic operators with triple characteristics of variable multiplicity [J].