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

被引：29

作者：

Danilov, VG ^{[1
]}

Maslov, VP

Shelkovich, VM

机构：

[1] Moscow Tech Univ Commun & Informat, Moscow, Russia

[2] Moscow MV Lomonosov State Univ, Moscow, Russia

[3] St Petersburg State Architecture & Civil Engn, St Petersburg, Russia

来源：

THEORETICAL AND MATHEMATICAL PHYSICS | 1998年 / 114卷 / 01期

基金：

俄罗斯基础研究基金会;

关键词：

D O I：

10.1007/BF02557106

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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 Hugoniot conditions for shock waves) and sufficient conditions for the existence of such solutions are obtained.

引用

页码：1 / 42

页数：42

共 50 条

[21] Singularities of Singular Solutions of First-Order Differential Equations of Clairaut Type
Kentaro Saji
Masatomo Takahashi
Journal of Dynamical and Control Systems, 2022, 28 : 19 - 41
[22] GLOBAL SOLUTIONS OF CAUCHY PROBLEM FOR QUASI-LINEAR FIRST-ORDER EQUATIONS IN SEVERAL SPACE VARIABLES
CONWAY, E
SMOLLER, J
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1966, 19 (01) : 95 - &
[23] QUASI-LINEAR HYPERBOLIC SYSTEMS WITH INVOLUTIONS
DAFERMOS, CM
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1986, 94 (04) : 373 - 389
[24] A QUASI-LINEAR, SINGULAR PERTURBATION PROBLEM OF HYPERBOLIC TYPE
VANHARTEN, A
VANHASSEL, RR
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1985, 16 (06) : 1258 - 1267
[25] BOUNDED SOLUTIONS AND SOLUTIONS PERIODIC IN A STRIP REGION TO QUASI-LINEAR HYPERBOLIC SYSTEMS
KIGURADZE, TI
DIFFERENTIAL EQUATIONS, 1994, 30 (10) : 1628 - 1639
[26] THE SINGULAR CAUCHY PROBLEM FOR A QUASI-LINEAR HYPERBOLIC EQUATION OF 2ND ORDER
OGAWA, H
JOURNAL OF MATHEMATICS AND MECHANICS, 1963, 12 (06): : 847 - 856
[27] A STUDY OF THE GLOBAL SOLUTIONS FOR QUASI-LINEAR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS
丁夏畦
张同
王靖华
肖玲
李才中
Science China Mathematics, 1973, (03) : 317 - 335
[28] Lipschitz continuous solutions to the Cauchy problem for quasi-linear hyperbolic systems
Xiang Chen
Chinese Annals of Mathematics, Series B, 2012, 33 : 521 - 536
[29] Positive periodic solutions of first-order singular systems
Chen, Ruipeng
Ma, Ruyun
He, Zhiqian
APPLIED MATHEMATICS AND COMPUTATION, 2012, 218 (23) : 11421 - 11428
[30] Lipschitz Continuous Solutions to the Cauchy Problem for Quasi-linear Hyperbolic Systems
Xiang CHEN11School of Mathematical Sciences
Chinese Annals of Mathematics(Series B), 2012, 33 (04) : 521 - 536

← 1 2 3 4 5 →