On the Cauchy problem for hyperbolic operators of second order whose coefficients depend only on the time variable

Seiichiro Wakabayashi

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On the Cauchy problem for hyperbolic operators of second order whose coefficients depend only on the time variable

机译：关于系数仅取决于时间变量的二阶双曲算子的柯西问题

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摘要

In this paper we deal with hyperbolic operators of second order whose coefficients depend only on the time variable and give necessary conditions and sufficient conditions for the Cauchy problem to be C~∝ well-posed. In particular, we give a necessary and sufficient condition (a complete characterization) for C~∝ well-posedness when the space dimension is equal to 2 and the coefficients are real analytic functions of the time variable.

机译：在本文中，我们处理二阶双曲算子，它们的系数仅取决于时间变量，并给出了柯西问题被适当提出的必要条件和充分条件。特别地，当空间维数等于2且系数是时间变量的真实解析函数时，我们给出C∝适定性的充要条件（完全表征）。

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来源
《Journal of the Mathematical Society of Japan》 |2010年第1期|95-133|共39页
作者
Seiichiro Wakabayashi;
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作者单位

Institute of Mathematics University of Tsukuba Tsukuba Ibaraki 305-8571 Japan;

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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类
关键词
cauchy problem; hyperbolic; C~∝ woll-posed; second order;

机译：柯西问题;双曲线C〜∝狼-的;二阶;

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2. Solvability of the Cauchy Problem for Linear Operator-Differential Equations with Variable Operator Coefficients [J] . M. K. Balaev Mathematical notes . 2011,第5a6期

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3. Short-Wave Asymptotics of Solutions of the Cauchy Problem for Hyperbolic Systems with Constant Coefficients and with Characteristics of Variable Multiplicity [J] . I. N. Shchitov Differential equations: A translation of differensial'nye uraveniya . 2014,第5期

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4. The Stokes phenomenon of the Cauchy problem for certain partial differential equations with variable coefficients depending on the time variable [C] . Bo?ena Tkacz Conference on Complex Differential and Difference Equations . 2020

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5. An admissible data class of the Cauchy problem for non-strictly hyperbolic operators [D] . Igari, Katsuju 1980

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7. On the Cauchy problem for hyperbolic operators of second order whose coefficients depend only on the time variable [O] . Seiichiro WAKABAYASHI 2010

机译：关于二阶的双曲算子Cauchy问题，其系数仅取决于时间变量

On the Cauchy problem for hyperbolic operators of second order whose coefficients depend only on the time variable

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