ISSN:
1420-9039
Keywords:
35L65
;
35L67
;
Conservation law
;
Riemann problem
;
viscous profile
;
nonuniqueness
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract We investigate a general mechanism, utilizing nonclassical shock waves, for nonuniqueness of solutions of Riemann initial-value problems for systems of two conservation laws. This nonuniqueness occurs whenever there exists a pair of viscous shock waves forming a 2-cycle, i.e., two statesU 1 andU 2 such that a traveling wave leads fromU 1 toU 2 and another leads fromU 2 toU 1. We prove that a 2-cycle gives rise to an open region of Riemann data for which there exist multiple solutions of the Riemann problem, and we determine all solutions within a certain class. We also present results from numerical experiments that illustrate how these solutions arise in the time-asymptotic limit of solutions of the conservation laws, as augmented by viscosity terms.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00920046
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