Geodesic
On exact justification of creeping wave solutions
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 13, Tome 128 (1983), pp. 48-64

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In this article the estimation of the difference between the Green function and the formal asymptotic solution in the shadow region is obtained. It is supposed that one of the points of source or observation is placed on the boundary and another one is outside from the boundary. The boundary is supposed to be the smooth convex curve. The case of Dirichlet problem is considered. 
@article{ZNSL_1983_128_a5,
     author = {A. B. Zayaev and V. B. Philippov},
     title = {On exact justification of creeping wave solutions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {48--64},
     publisher = {mathdoc},
     volume = {128},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1983_128_a5/}
}
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A. B. Zayaev; V. B. Philippov. On exact justification of creeping wave solutions. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 13, Tome 128 (1983), pp. 48-64. http://geodesic.mathdoc.fr/item/ZNSL_1983_128_a5/