V. G. Danilov, V. P. Maslov, V. M. Shelkovich, “Algebras of the singularities of singular solutions to first-order quasi-linear strictly hyperbolic systems”, TMF, 114:1 (1998), 3–55; Theoret. and Math. Phys., 114:1 (1998), 1

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Teoreticheskaya i Matematicheskaya Fizika, 1998, Volume 114, Number 1, Pages 3–55
DOI: https://doi.org/10.4213/tmf827 (Mi tmf827)

This article is cited in 51 scientific papers (total in 51 papers)

Algebras of the singularities of singular solutions to first-order quasi-linear strictly hyperbolic systems

V. G. Danilov^a, V. P. Maslov^b, V. M. Shelkovich^c

^a Moscow State Institute of Electronics and Mathematics (Technical University)
^b M. V. Lomonosov Moscow State University
^c St. Petersburg State University of Architecture and Civil Engineering

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DOI: https://doi.org/10.4213/tmf827

Abstract: An associative commutative algebra of distributions that contains homogeneous and associated homogeneous distributions is constructed. This algebra is used to analyze generalized solutions to strictly hyperbolic partial differential equations. Possible types of singularities are studied and the necessary (analogues of Hugoniуt conditions for shock waves) and sufficient conditions for the existence of such solutions are obtained.

Received: 29.07.1997

English version:
Theoretical and Mathematical Physics, 1998, Volume 114, Issue 1, Pages 1–42
DOI: https://doi.org/10.1007/BF02557106

Bibliographic databases:

Language: Russian

Citation: V. G. Danilov, V. P. Maslov, V. M. Shelkovich, “Algebras of the singularities of singular solutions to first-order quasi-linear strictly hyperbolic systems”, TMF, 114:1 (1998), 3–55; Theoret. and Math. Phys., 114:1 (1998), 1–42

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf827

https://doi.org/10.4213/tmf827

https://www.mathnet.ru/eng/tmf/v114/i1/p3

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Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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