On second order weakly hyperbolic equations and the ultradifferentiable classes

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• 作者：Fumihiko Hirosawa ; Haruhisa Ishida
• 刊名：Journal of Differential Equations
• 出版年：2013
• 出版时间：1 October, 2013
• 年：2013
• 卷：255
• 期：7
• 页码：1437-1468
• 全文大小：474 K

文摘

We consider second order weakly hyperbolic equations with time dependent coefficients in the ultradifferentiable classes. Our main purpose of the present paper is an investigation the relation between the classes of the functions to be well-posed and the following properties of the coefficients: the order of degeneration, stabilization to a monotonic function and their smoothness in the ultradifferentiable classes.