Abstract
The Cauchy problem for the wave equation in the case of discontinuity on the initial front is investigated. The discontinuity is described by a homogeneous generalized function of degree λ. The transformation of the initial front while passing the space-time caustic is studied. The structure of the wave front and the space-time rays near the caustic is considered. Bibliography: 4 titles.
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Literature Cited
N. Ya. Kirpichnikova, “Behavior of singularities of a nonsteady wave field near a caustic in a medium with a variable velocity,”Mathematical Problems of the Theory of Wave Propagation. 16, J. Sov. Math.,50, No. 4, 1743–1750 (1990).
N. Ya. Kirpichnikova, “Space-time caustic of an elastic short-wavelength field,”Mathematical Problems of the Theory of Wave Propagation. 12, J. Sov. Math.,24, No. 3 (1984).
V. M. Babich, V. S. Buldyrev, and I. A. Molotkov,Space-Time Ray Method: Linear and Nonlinear Waves [in Russian], Leningrad (1985).
V. M. Babich and V. S. Buldyrev,Asymptotic Methods in Problems of Short-Wave Diffraction [in Russian], Nauka, Moskow (1972).
Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 186, pp. 122–133, 1990.
Translated by N. Ya. Kirpichnikova.
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Kirpichnikova, N.Y. On the behavior near the caustic of a nonsteady wave field with singularity (A homogeneous generalized function) at the initial front. J Math Sci 73, 375–382 (1995). https://doi.org/10.1007/BF02362823
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DOI: https://doi.org/10.1007/BF02362823