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On the set of limit values of local diffeomorphisms in wavefront evolution

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Abstract

We study the problem of the appearance of nonsmooth singularities in the evolution of planar wavefronts in the Dirichlet problem for a first-order partial differential equation. The approach to investigating the singularities is based on the properties of local diffeomorphisms. A generalization of the classical notion of derivative is introduced, which coincides in particular cases with the Schwarz derivative. The results of modeling solutions of nonsmooth dynamic problems are presented.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Ural Division of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990, Russia

    A. A. Uspenskii & P. D. Lebedev

Authors
  1. A. A. Uspenskii
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  2. P. D. Lebedev
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Correspondence to A. A. Uspenskii.

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Original Russian Text © A.A. Uspenskii, P.D. Lebedev, 2010, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2010, Vol. 16, No. 1.

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Uspenskii, A.A., Lebedev, P.D. On the set of limit values of local diffeomorphisms in wavefront evolution. Proc. Steklov Inst. Math. 272 (Suppl 1), 255–270 (2011). https://doi.org/10.1134/S0081543811020180

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