ALGEBRAS OF THE SINGULARITIES OF SINGULAR SOLUTIONS TO FIRST-ORDER QUASI-LINEAR STRICTLY HYPERBOLIC SYSTEMS

Authors
DANILOV VG MASLOV VP SHELKOVICH VM
Citation
Vg. Danilov et al., ALGEBRAS OF THE SINGULARITIES OF SINGULAR SOLUTIONS TO FIRST-ORDER QUASI-LINEAR STRICTLY HYPERBOLIC SYSTEMS, Theoretical and mathematical physics, 114(1), 1998, pp. 1-42
Citations number
43
Categorie Soggetti
Physycs, Mathematical",Physics,"Physycs, Mathematical
Journal title
Theoretical and mathematical physics → ACNP
ISSN journal
00405779
Volume
114
Issue
1
Year of publication
1998
Pages
1 - 42
Database
ISI
SICI code
0040-5779(1998)114:1<1:AOTSOS>2.0.ZU;2-5
Abstract
An associative commutative algebra of distributions that contains homo geneous and associated homogeneous distributions is constructed. This algebra is used to analyze generalized solutions to strictly hyperboli c partial differential equations. Possible types of singularities are studied and the necessary (analogues of Hugoniot conditions for shock waves) and sufficient conditions for the existence of such solutions a re obtained.