The Riemann problem for general conservation laws

Author:
Tai Ping Liu

Journal:
Trans. Amer. Math. Soc. **199** (1974), 89-112

MSC:
Primary 35L65

MathSciNet review:
0367472

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The Riemann Problem for a system of hyperbolic conservation laws of form

**[1]**James Glimm,*Solutions in the large for nonlinear hyperbolic systems of equations*, Comm. Pure Appl. Math.**18**(1965), 697–715. MR**0194770****[2]**J. A. Smoller and J. L. Johnson,*Global solutions for an extended class of hyperbolic systems of conservation laws*, Arch. Rational Mech. Anal.**32**(1969), 169–189. MR**0236527****[3]**P. D. Lax,*Hyperbolic systems of conservation laws. II*, Comm. Pure Appl. Math.**10**(1957), 537–566. MR**0093653****[4]**Takaaki Nishida,*Global solution for an initial boundary value problem of a quasilinear hyperbolic system*, Proc. Japan Acad.**44**(1968), 642–646. MR**0236526****[5]**Takaaki Nishida and Joel A. Smoller,*Solutions in the large for some nonlinear hyperbolic conservation laws*, Comm. Pure Appl. Math.**26**(1973), 183–200. MR**0330789****[6]**O. A. Oleĭnik,*On the uniqueness of the generalized solution of the Cauchy problem for a non-linear system of equations occurring in mechanics*, Uspehi Mat. Nauk (N.S.)**12**(1957), no. 6(78), 169–176 (Russian). MR**0094543****[7]**J. A. Smoller,*On the solution of the Riemann problem with general step data for an extended class of hyperbolic systems*, Michigan Math. J.**16**(1969), 201–210. MR**0247283****[8]**J. A. Smoller,*A uniqueness theorem for Riemann problems*, Arch. Rational Mech. Anal.**33**(1969), 110–115. MR**0237961**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
35L65

Retrieve articles in all journals with MSC: 35L65

Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1974-0367472-1

Keywords:
Conservation laws,
shocks ,
rarefaction waves ,
contact discontinuities,
Oleinik condition (E),
Lax shock inequalities (L),
shock speed

Article copyright:
© Copyright 1974
American Mathematical Society