Journal for History of Mathematics (한국수학사학회지)

The Korean Society for History of Mathematics (한국수학사학회)
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Conservation Laws and Symmetry of Differential Equations -stories about E. Noether's Theorem-

보존률과 미분방정식의 대칭성 -뇌터의 정리를 중심으로-

  • Received : 2018.05.10
  • Accepted : 2018.10.10
  • Published : 2018.10.31
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Abstract

This paper surveys the theory of symmetry group of differential equations. A proof of the simplest version of the Noether's theorem on conservation laws has been presented with examples in the classical mechanics. As a new approach to the conservation laws the theory of characteristic cohomology due to S. H. Wang and others has been presented.

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References

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  2. R. BRYANT and P. GRIFFITHS, Characteristic cohomology of differential systems II, Conservation laws for a class of parabolic equations, Duke Math. J. 78 (1995), 531-676. https://doi.org/10.1215/S0012-7094-95-07824-7
  3. E. NOETHER, Invariante Variationsprobleme, Nachr. Konig. Gesell. Wissen. Gottingen, Math.-phys. Kl. (1918), 235-257. (발표 3년후 출판됨.) English translation: Transport Theory and Stat. Phys. (1) (1971), 186-207.
  4. P. Olver, Applications of Lie Groups to Differential Equations, 2nd Ed. Springer-Verlag, 1993.
  5. S.-H. WANG, Conservation laws from EDS point of view, Seoul N. Univ. Lecture-note, 2007.