Geodesic
On the asymptotics of Green's functions for certain wave problems. II. Nonstationary case
Sbornik. Mathematics, Tome 16 (1972) no. 1, pp. 45-59 
V. M. Babich. On the asymptotics of Green's functions for certain wave problems. II. Nonstationary case. Sbornik. Mathematics, Tome 16 (1972) no. 1, pp. 45-59. http://geodesic.mathdoc.fr/item/SM_1972_16_1_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Second part of the paper. The smoothness and the behavior at infinity in time of the Green's function of the wave equation for the exterior of a convex region is studied in this part. Figures: 4. Bibliography: 20 titles.

[1] V. M. Babich, “Ob asimptotike funktsii. Grina nekotorykh volnovykh zadach. I”, Matem. sb., 86(128) (1971), 518–537 | Zbl

[2] A. Ya. Povzner, I. V. Sukharevskii, “O razryvakh funktsii Grina smeshannoi zadachi dlya volnovogo uravneniya i o nekotorykh difraktsionnykh zadachakh”, DAN SSSR, 122:6 (1958) | MR | Zbl

[3] A. Ya. Povzner, I. V Sukharevskii, “O razryvakh funktsii Grina smeshannoi zadachi dlya volnogo uravneniya”, Matem. sb., 51(93) (1960), 3–26 | MR | Zbl

[4] C. S. Morawetz, D. Ludwig, “The generalized Huighens principle for reflecting bodies”, Comm. Pure and Appl. Math., 22:2 (1969), 189–205 | DOI | MR | Zbl

[5] V. M. Babich, “O korotkovolnovoi asimptotike funktsii Grina dlya uravneniya Gelmgoltsa”, Matem. sb., 65(107) (1964), 576–630 | Zbl

[6] F. Ursell, “On the short-wave asymptotic theory of the wave equation $(\nabla^2+k^2)\varphi=0$”, Proc. Cambridge Phil. Soc., 3:1 (1957), 115–133 | DOI | MR

[7] Grimshaw, “High-frequency scattering by finite convex regions”, Comm. Pure and Appl. Math., 19:2 (1966), 167–198 | DOI | MR | Zbl

[8] V. M. Babich, I. V. Olimpiev, Tretii simpozium po difraktsii voln, Nauka, Moskva, 1964

[9] I. V. Olimpiev, “Otsenki polya v oblasti teni pri difraktsii tsilindricheskoi volny na ogranichennom vypuklom tsilindre”, DAN SSSR, 156:5 (1964), 1068–1071 | MR | Zbl

[10] V. M. Babich, “Otsenka funktsii Grina dlya uravneniya Gelmgoltsa v zone teni”, Vestnik LGU, 7 (1965), 5–15 | Zbl

[11] D. Ludwig, “Uniform asymptotic expansion of the field scattered by a convex object of fTigh frequencies”, Comm. Pure and Appl. Math., 20:1 (1967), 103–138 | DOI | MR | Zbl

[12] C. S. Morawetz, D. Ludwig, “An inequality for reduced wave operator and the justification of geometrical optics”, Comm. Pure and Appl. Math., 21:2 (1968), 111–118 | DOI | MR

[13] V. M. Babich, “Ob analiticheskom prodolzhenii rezolventy vneshnikh zadach dlya operatora Laplasa na vtoroi list”, Teoriya funktsii, funkts. analiz i ikh prilozheniya, 3, LGU, Leningrad, 1966, 151–157

[14] F. I. Fridlender, Zvukovye impulsy, IL, Moskva, 1962

[15] H. Reichardt, “Ausstrahlungsbedingungen fur die Wellengleichung”, Abhandl Math. Seminar Univ., 24, Hamburg, 1960, 41–53 | MR | Zbl

[16] R. C. Mac Camy, “Low frequency acoustic oscillations”, Quart. Appl. Math., 23:3 (1965), 247–255 | MR | Zbl

[17] O. A. Ladyzhenskaya, “O printsipe predelnoi amplitudy”, Uspekhi matem. nauk, XII:3(75) (1957), 161–164

[18] N. D. Kazarinoff, R. K. Rill, “Scalar diffraction theory and turning point problems”, ARMA, 5:2 (1960), 177–186 | DOI | MR | Zbl

[19] C. S. Morawetz, “The limiting amplitude principle”, Comm. Pure and Appl. Math., 15:3 (1962), 249–361 | DOI | MR

[20] E. Zachmanoglou, “The decay of solutions of the initial-boundary value problem for the wave equation in unbounded regions”, ARMA, 14:4 (1963), 312–325 | MR | Zbl