Science China Mathematics

, Volume 61, Issue 11, pp 1947–1962 | Cite as

Normal forms of linear second order partial differential equations on the plane

  • Alexey Davydov
Open Access


The paper is devoted to the theory of normal forms of main symbols for linear second order partial differential equations on the plane. We discuss the results obtained in the last decades and some problems, which are important both for the development of this theory and the applications. The reduction theorem, which was used to obtain many of recent results in the theory, is included in the paper in the parametric form together with proof. There is a feeling that the theorem still has potential to get progress in the solution of open problems in the theory.


normal form mixed type partial differential equation main symbol 


34A09 34C20 



This work was supported by the Ministry of Education and Science of the Russian Federation (Grant No. 1.638.2016/FPM).

Open access funding provided by International Institute for Applied Systems Analysis (IIASA).


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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Department of MathematicsThe National University of Science and Technology MISiSMoscowRussia
  2. 2.Department of Theory of Dynamical SystemsLomonosov Moscow State UniversityMoscowRussia
  3. 3.International Institute for Applied Systems AnalysisLaxenburgAustria

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