Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Existence and uniqueness theorems for Riemann problems

Author: Tai Ping Liu
Journal: Trans. Amer. Math. Soc. 212 (1975), 375-382
MSC: Primary 35L65
MathSciNet review: 0380135
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In [2] the author proposed the entropy condition (E) and solved the Riemann problem for general $ 2 \times 2$ conservation laws $ {u_t} + f{(u,v)_x} = 0,{v_t} + g{(u,v)_x} = 0$, under the assumptions that the system is hyperbolic, and $ {f_u} \geqslant 0$ and $ {g_v} \leqslant 0$. The purpose of this paper is to extend the above results to a much wider class of $ 2 \times 2$ conservation laws. Instead of assuming that $ {f_u} \geqslant 0$ and $ {g_v} \leqslant 0$, we assume that the characteristic speed is not equal to the shock speed of different family. This assumption is motivated by the works of Lax [1] and Smoller [4].

References [Enhancements On Off] (What's this?)

Similar Articles

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

Retrieve articles in all journals with MSC: 35L65

Additional Information

Keywords: Conservation laws, shocks, rarefaction waves, contact discontinuities, Lax shock inequalities (L), entropy condition (E)
Article copyright: © Copyright 1975 American Mathematical Society