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On uniform quasiasymptotics of solutions of the second mixed problem for a hyperbolic equation. (English. Russian original) Zbl 0635.35056
Math. USSR, Sb. 59, No. 2, 409-427 (1988); translation from Mat. Sb., Nov. Ser. 131(173), No. 4(12), 419-437 (1986).
The paper is dedicated to the initial value problem and the second mixed boundary value problem for linear multidimensional hyperbolic equations with a uniformly elliptic operator depending on space variables only. The asymptotic (for \(t\to +\infty)\) behaviour of the solution in question is estimated by uniform quasi asymptotics of a given order. The two theorems are proved on necessary and sufficient conditions, under which the solutions of both problems mentioned above have the uniform quasi asymptotics. These conditions contain the requirements to the right-hand side of partial differential equation and to initial functions. 13 references fully cover the considered problem.
Reviewer: V.Chernyatin

MSC:
35L20 Initial-boundary value problems for second-order hyperbolic equations
35L15 Initial value problems for second-order hyperbolic equations
35B40 Asymptotic behavior of solutions to PDEs
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