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On uniform quasisymptotics of the solution of the Cauchy problem for a hyperbolic equation. (English. Russian original) Zbl 0629.35072
Sov. Math., Dokl. 33, 326-329 (1986); translation from Dokl. Akad. Nauk SSSR 287, 37-40 (1986).
The problem under investigation is the behavior of the solution of the following Cauchy problem \[ p(x)u_{tt}-\Delta u=f(x,t),\quad (x,t)\in R^ n\times R;\quad u|_{t=0}=\phi (x),\quad u_ t|_{t=0}=\psi (x) \] for large time. It is given a definition of the uniform quasiasymptotics. Using this notion a theorem is formulated which reduces the general problem to a more simple one. The main steps of the proof is sketched and some special cases are regarded as well as a one dimensional problem.
Reviewer: G.Molnarka

35L15 Initial value problems for second-order hyperbolic equations
35B40 Asymptotic behavior of solutions to PDEs