一元空间变量中适当双曲型方程的柯西问题

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED Journal of Hyperbolic Differential Equations Pub Date : 2021-10-07 DOI:10.1142/S0219891622500138

Sergio Spagnolo Giovanni Taglialatela

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引用次数: 2

摘要

在本文中，我们考虑了高阶弱双曲型方程的柯西问题，假设主符号仅依赖于一个空间变量，并且特征根[公式：见正文]验证了类似[公式：看正文]的不等式。我们证明了如果具有冻结系数的算子在Gårding。

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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The Cauchy problem for properly hyperbolic equations in one space variable

In 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 [Formula: see text] verify an inequality like [Formula: see text] We prove that the Cauchy problem is well-posed in [Formula: see text] if the operators with frozen coefficients are uniformly hyperbolic in the sense of Gårding.

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来源期刊

Journal of Hyperbolic Differential Equations 数学-物理：数学物理

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： This journal publishes original research papers on nonlinear hyperbolic problems and related topics, of mathematical and/or physical interest. Specifically, it invites papers on the theory and numerical analysis of hyperbolic conservation laws and of hyperbolic partial differential equations arising in mathematical physics. The Journal welcomes contributions in: Theory of nonlinear hyperbolic systems of conservation laws, addressing the issues of well-posedness and qualitative behavior of solutions, in one or several space dimensions. Hyperbolic differential equations of mathematical physics, such as the Einstein equations of general relativity, Dirac equations, Maxwell equations, relativistic fluid models, etc. Lorentzian geometry, particularly global geometric and causal theoretic aspects of spacetimes satisfying the Einstein equations. Nonlinear hyperbolic systems arising in continuum physics such as: hyperbolic models of fluid dynamics, mixed models of transonic flows, etc. General problems that are dominated (but not exclusively driven) by finite speed phenomena, such as dissipative and dispersive perturbations of hyperbolic systems, and models from statistical mechanics and other probabilistic models relevant to the derivation of fluid dynamical equations. Convergence analysis of numerical methods for hyperbolic equations: finite difference schemes, finite volumes schemes, etc.

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