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 Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 2, Pages 411–424 (Mi izv1248)

On Maslov's method for constructing combined asymptotics for $h$-pseudodifferential equations

V. G. Danilov, P. N. Zhevandrov

Abstract: The authors discuss a scheme proposed by V. P. Maslov for constructing combined (with respect to smoothness and a small parameter $h$) asymptotics of the solution of the Cauchy problem for $h$-pseudodifferential equations. The exposition is carried out by means of examples of equations for the oscillations of a crystal lattice and for water waves. The main attention is given to the isolation of the leading term of the asymptotics. A number of estimates are proved for the remainders in formulas for the action of an $h$-pseudodifferential operator on the exponential function, with respect to smoothness and the parameter.
Bibliography: 9 titles

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English version:
Mathematics of the USSR-Izvestiya, 1990, 34:2, 425–439

Bibliographic databases:

UDC: 517.9
MSC: Primary 35S10, 35B40; Secondary 34E20, 76B15, 35L15

Citation: V. G. Danilov, P. N. Zhevandrov, “On Maslov's method for constructing combined asymptotics for $h$-pseudodifferential equations”, Izv. Akad. Nauk SSSR Ser. Mat., 53:2 (1989), 411–424; Math. USSR-Izv., 34:2 (1990), 425–439

Citation in format AMSBIB
\Bibitem{DanZhe89} \by V.~G.~Danilov, P.~N.~Zhevandrov \paper On Maslov's method for constructing combined asymptotics for $h$-pseudodifferential equations \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1989 \vol 53 \issue 2 \pages 411--424 \mathnet{http://mi.mathnet.ru/izv1248} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=998304} \zmath{https://zbmath.org/?q=an:0703.35185} \transl \jour Math. USSR-Izv. \yr 1990 \vol 34 \issue 2 \pages 425--439 \crossref{https://doi.org/10.1070/IM1990v034n02ABEH000659}