Hyperbolic Equations in the Twentieth Century
Hyperbolic Equations in the Twentieth Century
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二十世纪的双曲方程
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
L. Gårding
中科院分区：
文献类型：
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作者：
L. Gårding
这个主题开始于惠更斯的波前理论，作为更平滑的波的包络，以及欧拉的后续工作，在阿达玛的“局部精细”理论之前，波阵面处的奇点是不被理解的。Herglotz和Petrovsky的贡献以及Laurent Schwartz在40年代创立的分布理论极大地启发了对非线性系统解的奇点的研究本文讨论了Hadamard，Schauder，Petrovsky和作者提出的Cauchy问题的解，以及最近由M.Sato提出的微局部分析
The subject began with Huygens’s theory of wave fronts as envelopes of smoother waves, and subsequent work by Euler, d’Alembert and Riemann.Singularities at the wave fronts were not understood before Hadamard’s theory of “partie finie” at the beginning of this century.Contributions by Herglotz and Petrovsky and the theory of distributions created in the forties by Laurent Schwartz greatly illuminated the study of singularities of solutions of hyperbolic PDE’s.Solutions of Cauchy’s problem given by Hadamard, Schauder, Petrovsky, and the author are discussed.More recently, microlocal analysis, initiated by M.Sato