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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2010, Volume 16, Number 1, Pages 171–185 (Mi timm536)  
This article is cited in 16 scientific papers (total in 16 papers)

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

A. A. Uspenskii, P. D. Lebedev

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Full-text PDF (455 kB) Citations (16)
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Abstract: We study the problem of the appearance of nonsmooth singularities in the evolution of plane 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 a derivative is introduced, which coincides in particular cases with the Schwarz derivative. The results of modeling solutions of nonsmooth dynamic problems are presented.
Keywords: first-order partial differential equation, minimax solution, diffeomorphism, eikonal, optimal result function, symmetry set.
Received: 17.11.2009
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2011, Volume 272, Issue 1, Pages S255–S270
DOI: https://doi.org/10.1134/S0081543811020180
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: A. A. Uspenskii, P. D. Lebedev, “On the set of limit values of local diffeomorphisms in wavefront evolution”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 1, 2010, 171–185; Proc. Steklov Inst. Math. (Suppl.), 272, suppl. 1 (2011), S255–S270
Citation in format AMSBIB
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\paper On the set of limit values of local diffeomorphisms in wavefront evolution
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\pages 171--185
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\jour Proc. Steklov Inst. Math. (Suppl.)
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\pages S255--S270
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    • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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