Geodesic
On the uniform quasiasymptotics of the solutions of hyperbolic equations
Sbornik. Mathematics, Tome 70 (1991) no. 1, pp. 109-128

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The uniform quasiasymptotics as $t\to\infty$ of the solutions of the second mixed problem and of the Cauchy problem for a linear hyperbolic second order equation are studied in the scale of self-similar functions. The method of investigation is based on the construction, in terms of a given self-similar function, of a special convolution operator that reduces the study of the quasiasymptotics to that of the power scale case discussed earlier. 
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     author = {V. Zh. Dumanyan},
     title = {On the uniform quasiasymptotics of the solutions of hyperbolic equations},
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V. Zh. Dumanyan. On the uniform quasiasymptotics of the solutions of hyperbolic equations. Sbornik. Mathematics, Tome 70 (1991) no. 1, pp. 109-128. http://geodesic.mathdoc.fr/item/SM_1991_70_1_a7/