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TMF, 1998, Volume 114, Number 1, Pages 3–55 (Mi tmf827)  

This article is cited in 38 scientific papers (total in 38 papers)

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

V. G. Danilova, V. P. Maslovb, V. M. Shelkovichc

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

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.


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Theoretical and Mathematical Physics, 1998, 114:1, 1–42

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Received: 29.07.1997

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
\by V.~G.~Danilov, V.~P.~Maslov, V.~M.~Shelkovich
\paper Algebras of the singularities of singular solutions to first-order quasi-linear strictly hyperbolic systems
\jour TMF
\yr 1998
\vol 114
\issue 1
\pages 3--55
\jour Theoret. and Math. Phys.
\yr 1998
\vol 114
\issue 1
\pages 1--42

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    3. Dobrokhotov, SY, “On Maslov's conjecture about the structure of weak point singularities of shallow-water equations”, Doklady Mathematics, 64:1 (2001), 127  mathscinet  zmath  isi
    4. Dobrokhotov, SY, “Proof of Maslov's conjecture about the structure of weak point singular solutions of the shallow water equations”, Russian Journal of Mathematical Physics, 8:1 (2001), 25  mathscinet  zmath  isi
    5. Danilov V.G., Shelkovich V.M., “Propagation and interaction of nonlinear waves to quasilinear equations”, Hyperbolic Problems: Theory, Numerics, Applications, International Series of Numerical Mathematics, 140, 2001, 267–276  mathscinet  isi
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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