Abstract
The Cauchy problem for the wave equation is considered. A discontinuity in the form of a homogeneous generalized function of degree λ is given at the initial front. An asymptotic solution is found in the vicinity of the space-time caustic in the interaction of the discontinuity surface with the caustic. The solution is represented in the form of a certain combination of the generalized function with associated Legendre polynomials.
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Literature cited
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 156, pp. 98–108, 1986.
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Kirpichnikova, N.Y. Behavior of singularities of a nonsteady wave field near a caustic in a medium with a variable velocity. J Math Sci 50, 1743–1750 (1990). https://doi.org/10.1007/BF01097104
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DOI: https://doi.org/10.1007/BF01097104