Golubeva, A. S. Solutions of the membrane equation concentrated near extremal loops. (English. Russian original) Zbl 0900.35115 J. Math. Sci., New York 91, No. 2, 2725-2732 (1998); translation from Zap. Nauchn. Semin. POMI 230, 41-51 (1995). Summary: Formal asymptotic solutions of the equation \(\Delta^2u- (\omega^4/c^4(x,y))u=0\) concentrated near extremal cycles with \(N\geq 2\) corners are constructed by application of the complex ray method. Cited in 1 ReviewCited in 2 Documents MSC: 35J30 Higher-order elliptic equations 35C20 Asymptotic expansions of solutions to PDEs Keywords:asymptotic solutions; complex ray method PDFBibTeX XMLCite \textit{A. S. Golubeva}, J. Math. Sci., New York 91, No. 2, 2725--2732 (1995; Zbl 0900.35115); translation from Zap. Nauchn. Semin. POMI 230, 41--51 (1995) Full Text: DOI References: [1] I. M. Babakov,Theory of Oscillations [in Russian], Moscow (1968). [2] V. M. Babie and V. S. Buldyrev,Short-Wavelength Diffraction Theory, Springer-Verlag, Berlin (1991). [3] M. M. Popov, ”Asymptotics of certain subsequences of eigenvalues of boundary-value problems for the Helmholtz equation in the multidimensional case,”Dokl. Akad. Nauk SSSR,184, 1076–1097 (1969). [4] V. E. Nomofilov, ”Asymptotic solutions of systems of second-order equations concentrated near a ray,”Zap. Nauchn. Semin. LOMI,104, 170–179 (1981). · Zbl 0476.58029 [5] P. K. Rashevskii,Lectures on Differential Geometry [in Russian], Gostekhizdat (1956). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.