Hyperbolic equations with non-analytic coefficients

被引：26

作者：

Kinoshita, Tamotu

Spagnolo, Sergio ^{[1
]}

机构：

[1] Univ Tsukuba, Inst Math, Tsukuba, Ibaraki 3058571, Japan

[2] Univ Pisa, Dept Math L Tonelli, I-56127 Pisa, Italy

来源：

MATHEMATISCHE ANNALEN | 2006年 / 336卷 / 03期

关键词：

D O I：

10.1007/s00208-006-0009-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that the Cauchy problem for a hyperbolic, homogeneous equation with C-infinity coefficients depending on time, is well posed in every Gevrey class, although in general it is not well-posed in C-infinity, provided the characteristic roots satisfy the condition lambda(i)(t)(2) +lambda(j)(t)(2) <= M(lambda(i)(t) -lambda(j)(t))(2) (i not equal j).

引用

页码：551 / 569

页数：19

共 15 条

[1]

[Anonymous], 1983, ANN SCUOLA NORM-SCI

[2]

Bronshtein M. D., 1982, T MOSCOW MATH SOC, V1, P87

[3] AN EXAMPLE OF A WEAKLY HYPERBOLIC CAUCHY-PROBLEM NOT WELL POSED IN C-INFINITY [J].