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)

 

 

Systems of conservation laws with invariant submanifolds


Author: Blake Temple
Journal: Trans. Amer. Math. Soc. 280 (1983), 781-795
MSC: Primary 35L67; Secondary 73C50, 76S05
DOI: https://doi.org/10.1090/S0002-9947-1983-0716850-2
MathSciNet review: 716850
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Systems of conservation laws with coinciding shock and rarefaction curves arise in the study of oil reservoir simulation, multicomponent chromatography, as well as in the study of nonlinear motion in elastic strings. Here we characterize this phenomenon by deriving necessary and sufficient conditions on the geometry of a wave curve in order that the shock wave curve coincide with its associated rarefaction wave curve for a system of conservation laws. This coincidence is the one dimensional case of a submanifold of the state variables being invariant for the system of equations, and the necessary and sufficient conditions are derived for invariant submanifolds of arbitrary dimension. In the case of $ 2 \times 2$ systems we derive explicit formulas for the class of flux functions that give rise to the coupled nonlinear conservation laws for which the shock and rarefaction wave curves coincide.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 35L67, 73C50, 76S05

Retrieve articles in all journals with MSC: 35L67, 73C50, 76S05


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1983-0716850-2
Article copyright: © Copyright 1983 American Mathematical Society