Geodesic
On the uniform quasiasymptotics of the solutions of hyperbolic equations
Sbornik. Mathematics, Tome 70 (1991) no. 1, pp. 109-128 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] Guschin A. K., Mikhailov V. P., “O ravnomernoi kvaziasimptotike reshenii vtoroi smeshannoi zadachi dlya giperbolicheskogo uravneniya”, Matem. sb., 131(173) (1986), 419–437 | Zbl

[2] Guschin A. K., Mikhailov V. P., “Teoremy sravneniya dlya reshenii giperbolicheskikh uravnenii”, Matem. sb., 134(176) (1987), 363–374

[3] Guschin A. K., Mikhailov V. P., “O ravnomernoi kvaziasimptotike resheniya zadachi Koshi dlya giperbolicheskogo uravneniya”, DAN SSSR, 287:1 (1986), 37–40 | MR | Zbl

[4] Guschin A. K., Mikhailov V. P., “O ravnomernoi kvazistabilizatsii resheniya zadachi Koshi dlya giperbolicheskogo uravneniya”, DAN SSSR, 276:3 (1984), 532–535 | MR | Zbl

[5] Guschin A. K., Mikhailov V. P., “O ravnomernoi stabilizatsii resheniya zadachi Koshi dlya giperbolicheskogo uravneniya vtorogo poryadka”, Tr. MIAN, 166 (1984), 76–90 | Zbl

[6] Mikhailov Yu. A., “O ravnomernoi kvazistabilizatsii reshenii vtoroi smeshannoi zadachi dlya giperbolicheskogo uravneniya”, DAN SSSR, 287:1 (1986), 45–49 | MR

[7] Mikhailov Yu. A., “O ravnomernoi kvazistabilizatsii resheniya vtoroi smeshannoi zadachi dlya giperbolicheskogo uravneniya vtorogo poryadka”, Matem. sb., 129(171) (1986), 232–251 | MR

[8] Zavyalov B. I., “Avtomodelnaya asimptotika elektromagnitnykh form-faktorov i povedenie ikh Fure-obrazov v okrestnosti svetovogo konusa”, TMF, 17:2 (1973), 178–188

[9] Drozhzhinov Yu. N., Zavyalov B. I., “Kvaziasimptotika obobschennykh funktsii i tauberovye teoremy v kompleksnoi oblasti”, Matem. sb., 102(144) (1977), 372–390 | Zbl

[10] Drozhzhinov Yu. N., Zavyalov B. I., “Asimptoticheskie svoistva nekotorykh klassov obobschennykh funktsii”, Izv. AN SSSR. Ser. matem., 49:1 (1985), 81–140 | MR

[11] Vladimirov V. S., Drozhzhinov Yu. N., Zavyalov B. I., Mnogomernye tauberovye teoremy dlya obobschennykh funktsii, Nauka, M., 1986 | MR

[12] Seneta E., Regulary varying functions, Lect. Notes in Math., 508, Springer-Verlag, Berlin, 1976 ; Seneta E., Pravilno menyayuschiesya funktsii, Nauka, M., 1985 | MR | Zbl | MR | Zbl

[13] Prudnikov A. P., Brychkov Yu. A., Marichev O. I., Integraly i ryady, Nauka, M., 1981 | MR | Zbl