Systems of conservation laws with invariant submanifolds
Author:
Blake Temple
Journal:
Trans. Amer. Math. Soc. 280 (1983), 781795
MSC:
Primary 35L67; Secondary 73C50, 76S05
MathSciNet review:
716850
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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 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.
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 E. Isaacson, Global solution of a Riemann problem for a nonstrictly hyperbolic system of conservation laws arising in enhanced oil recovery, J. Comput. Phys. (to appear).
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 C. Conley, J. Smoller and K. Chueh, Positively invariant regions for systems of nonlinear reaction diffusion equations, Indiana Univ. Math. J. 26 (1977). MR 0430536 (55:3541)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947198307168502
PII:
S 00029947(1983)07168502
Article copyright:
© Copyright 1983
American Mathematical Society
