On Maslov's method for constructing combined asymptotics for $h$-pseudodifferential equations
V. G. Danilov, P. N. Zhevandrov
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.
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Mathematics of the USSR-Izvestiya, 1990, 34:2, 425–439
MSC: Primary 35S10, 35B40; Secondary 34E20, 76B15, 35L15
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
\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.
\jour Math. USSR-Izv.
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