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Non-standard characteristics in asymptotic problems. (English. Russian original) Zbl 0562.35007
Russ. Math. Surv. 38, No. 6, 1-42 (1983); translation from Usp. Mat. Nauk. 38, No. 6(234), 3-36 (1983).
The author gives a more general definition of characteristics. Using this definition it is possible to connect different domains of mathematics and physics. The paper contains principal ideas connected with the construction of non-standard characteristics and the solution of suitable asymptotic problems. The author presents a lot of examples. The paper is some kind of a survey.
Reviewer: W.Okrasiński

MSC:
35A30 Geometric theory, characteristics, transformations in context of PDEs
35S05 Pseudodifferential operators as generalizations of partial differential operators
47Gxx Integral, integro-differential, and pseudodifferential operators
58J40 Pseudodifferential and Fourier integral operators on manifolds
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