Algebras of the singularities of singular solutions to first-order quasi-linear strictly hyperbolic systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 114 (1998) no. 1, pp. 3-55
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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.
@article{TMF_1998_114_1_a0,
author = {V. G. Danilov and V. P. Maslov and V. M. Shelkovich},
title = {Algebras of the singularities of singular solutions to first-order quasi-linear strictly hyperbolic systems},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {3--55},
publisher = {mathdoc},
volume = {114},
number = {1},
year = {1998},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1998_114_1_a0/}
}
TY - JOUR AU - V. G. Danilov AU - V. P. Maslov AU - V. M. Shelkovich TI - Algebras of the singularities of singular solutions to first-order quasi-linear strictly hyperbolic systems JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1998 SP - 3 EP - 55 VL - 114 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1998_114_1_a0/ LA - ru ID - TMF_1998_114_1_a0 ER -
%0 Journal Article %A V. G. Danilov %A V. P. Maslov %A V. M. Shelkovich %T Algebras of the singularities of singular solutions to first-order quasi-linear strictly hyperbolic systems %J Teoretičeskaâ i matematičeskaâ fizika %D 1998 %P 3-55 %V 114 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_1998_114_1_a0/ %G ru %F TMF_1998_114_1_a0
V. G. Danilov; V. P. Maslov; V. M. Shelkovich. Algebras of the singularities of singular solutions to first-order quasi-linear strictly hyperbolic systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 114 (1998) no. 1, pp. 3-55. http://geodesic.mathdoc.fr/item/TMF_1998_114_1_a0/