Semi-discrete shock profiles for hyperbolic systems of conservation laws

被引：23

作者：

Benzoni-Gavage, S ^{[1
]}

机构：

[1] Ecole Normale Super Lyon, CNRS, UMR 128, F-69364 Lyon 07, France

来源：

PHYSICA D | 1998年 / 115卷 / 1-2期

关键词：

systems of conservation laws; shock waves; numerical schemes; retarded functional differential equations;

D O I：

10.1016/S0167-2789(97)00225-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The existence of semi-discrete shock profiles for a general hyperbolic system of conservation laws is proved. Such profiles are regarded as heteroclinic orbits of a retarded functional differential equation (RFDE). The proof relies on the Hale center manifold theorem and holds for shocks of small strength. Copyright (C) 1998 Elsevier Science B.V.

引用

页码：109 / 123

页数：15

共 14 条

[1] STEADY STATE SOLUTIONS OF HYPERBOLIC SYSTEMS OF CONSERVATION LAWS WITH VISCOSITY TERMS [J].

FOY, LR .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1964, 17 (02) :177-&

[2]

Godunov SK., 1959, MAT SBORNIK, V89, P271

[3] NONLINEAR ASYMPTOTIC STABILITY OF VISCOUS SHOCK PROFILES FOR CONSERVATION-LAWS [J].

GOODMAN, J .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1986, 95 (04) :325-344

[4]

Hale J. K., 1993, INTRO FUNCTIONAL DIF, DOI 10.1007/978-1-4612-4342-7

[5] VARIATIONAL STUDY OF THE RIEMANN PROBLEM [J].

HEIBIG, A ;

SERRE, D .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1992, 96 (01) :56-88

[6] DISCRETE SHOCKS [J].

JENNINGS, G .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1974, 27 (01) :25-37

[7] HYPERBOLIC SYSTEMS OF CONSERVATION LAWS .2. [J].

LAX, PD .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1957, 10 (04) :537-566

[8] NONLINEAR STABILITY OF DISCRETE SHOCKS FOR SYSTEMS OF CONSERVATION-LAWS [J].

LIU, JG ;

XIN, ZP .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1993, 125 (03) :217-256

[9] DISCRETE SHOCK PROFILES FOR SYSTEMS OF CONSERVATION-LAWS [J].

MAJDA, A ;

RALSTON, J .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1979, 32 (04) :445-482

[10] DISCRETE SHOCKS FOR DIFFERENCE APPROXIMATIONS TO SYSTEMS OF CONSERVATION-LAWS [J].

MICHELSON, D .

ADVANCES IN APPLIED MATHEMATICS, 1984, 5 (04) :433-469

← 1 2 →