A more direct way to the Cauchy problem for effectively hyperbolic operators

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Pseudo-Differential Operators and Applications Pub Date : 2024-03-15 DOI:10.1007/s11868-024-00592-4

引用次数: 0

Abstract

This paper is devoted to a simpler derivation of energy estimates and a proof of the well-posedness, compared to previously existing ones, for effectively hyperbolic Cauchy problem. One difference is that instead of using the general Fourier integral operator, we only use a change of local coordinates x (of the configuration space) leaving the time variable invariant. Another difference is an efficient application of the Weyl-Hörmander calculus of pseudodifferential operators associated with several different metrics.

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有效双曲算子考奇问题的更直接方法

摘要本文致力于对有效双曲 Cauchy 问题的能量估计进行更简单的推导，并证明其良好求解性。其中一个区别是，我们没有使用一般的傅里叶积分算子，而只使用了局部坐标 x（配置空间）的变化，时间变量保持不变。另一个不同之处是，我们有效地应用了与多个不同度量相关的伪微分算子的韦尔-赫曼德微积分。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Pseudo-Differential Operators and Applications MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.20

自引率

9.10%

发文量

期刊介绍： The Journal of Pseudo-Differential Operators and Applications is a forum for high quality papers in the mathematics, applications and numerical analysis of pseudo-differential operators. Pseudo-differential operators are understood in a very broad sense embracing but not limited to harmonic analysis, functional analysis, operator theory and algebras, partial differential equations, geometry, mathematical physics and novel applications in engineering, geophysics and medical sciences.