A CONTRACTIVE METRIC FOR SYSTEMS OF CONSERVATION-LAWS WITH COINCIDING SHOCK AND RAREFACTION CURVES

被引：16

作者：

BRESSAN, A

机构：

[1] Sissa, I 34014 Trieste

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 1993年 / 106卷 / 02期

关键词：

D O I：

10.1006/jdeq.1993.1111

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce two algorithms for the construction of weak, entropy-admissible solutions to a class of systems of conservation laws with coinciding shock and rarefaction curves. Global existence, uniqueness, and continuous dependence are proved for all solutions obtained by our constructive procedure. The generated semigroup is contractive with respect to a Riemann-type metric, defined in terms of Glimm′s wave interaction functional, equivalent to the usual L1 distance. © 1993 Academic Press. All rights reserved.

引用

页码：332 / 366

页数：35

共 18 条

[1] CONTRACTIVE METRICS FOR NONLINEAR HYPERBOLIC SYSTEMS [J].

BRESSAN, A .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1988, 37 (02) :409-421

[2] GLOBAL-SOLUTIONS OF SYSTEMS OF CONSERVATION-LAWS BY WAVE-FRONT TRACKING [J].

BRESSAN, A .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1992, 170 (02) :414-432

[3] SEMIGROUP APPROACH TO FIRST-ORDER QUASILINEAR EQUATIONS IN SEVERAL SPACE VARIABLES [J].

CRANDALL, MG .

ISRAEL JOURNAL OF MATHEMATICS, 1972, 12 (02) :108-&

[4] GENERALIZED CHARACTERISTICS UNIQUENESS AND REGULARITY OF SOLUTIONS IN A HYPERBOLIC SYSTEM OF CONSERVATION-LAWS [J].

DAFERMOS, CM ;

GENG, X .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1991, 8 (3-4) :231-269

[5] POLYGONAL APPROXIMATIONS OF SOLUTIONS OF INITIAL VALUE-PROBLEM FOR A CONSERVATION LAW [J].

DAFERMOS, CM .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1972, 38 (01) :33-&

[6] GLOBAL EXISTENCE OF SOLUTIONS TO NONLINEAR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS [J].

DIPERNA, RJ .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1976, 20 (01) :187-212

[7] UNIQUENESS OF SOLUTIONS TO HYPERBOLIC CONSERVATION-LAWS [J].

DIPERNA, RJ .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1979, 28 (01) :137-188

[8]

GLIMM J, 1965, COMMUN PUR APPL MATH, V18, P95

[9]

JOHN F, 1965, COMMUN PUR APPL MATH, V18, P95

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

LAX, PD .

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

← 1 2 →