Geodesic
On the asymptotics of Green's functions for certain wave problems. I. Stationary case
Sbornik. Mathematics, Tome 15 (1971) no. 4, pp. 513-533 
V. M. Babich. On the asymptotics of Green's functions for certain wave problems. I. Stationary case. Sbornik. Mathematics, Tome 15 (1971) no. 4, pp. 513-533. http://geodesic.mathdoc.fr/item/SM_1971_15_4_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

First part of paper. The paper is concerned with the study of asymptotic properties of the Green function for the Neumann problem in the exterior of a planar convex domain for the Helmholtz equation. Figures: 1. Bibliography: 8 titles.

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

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

[3] F. Ursell, “On the short-wave asymptotic theory of the wave equation $(V^2+k^2)\varphi=0$”, Proc. Cambr. Phil. Soc., 53:1 (1957), 115–133 | DOI | MR | Zbl

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

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

[6] V. D. Andronov, Nekotorye primeneniya metoda Ersela v korotkovolnovykh zadachakh dlya uravneniya Gelmgoltsa, Dissertatsiya, LGU, Leningrad, 1965

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

[8] V. M. Babich, “Otsenka funktsii Grina dlya uravneniya Gelmgoltsa v zone teni”, Vestnik LGU, 1965, no. 7, 5–15 | Zbl