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U.S. Department of Energy
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Geometric theory of infinite-dimensional dynamical systems. Final report, 15 Aug 88-14 Oct 91

Technical Report ·
OSTI ID:7081598
A subject of investigation was the extent to which an entropy inequality (i.e., the Second Law of Thermodynamics) induces stabilization of solutions of hyperbolic systems of conservation laws. It was shown that the entropy inequality guarantees uniqueness of Lipschitz solutions within the class of BV solutions, provided that the entropy is convex just in certain directions compatible with the natural invariance of the system expressed in terms of involutions . It was proven that BV solutions of strictly hyperbolic systems with shocks of moderate strength, which satisfy the Liu admissibility condition, minimize the rate of total entropy production. The theory of generalized characteristics for a single conservation law, developed earlier by the author, was applied to conservation laws with inhomogeneity and fading memory. The theory of generalized characteristics was developed for systems of conservations laws and was used to obtain information on the large time behavior of solutions. This theory was employed to establish uniqueness of solutions for special systems of conservation laws in which shock and rarefaction wave curves coincide.
Research Organization:
Brown Univ., Providence, RI (United States). Div. of Applied Mathematics
OSTI ID:
7081598
Report Number(s):
AD-A-252190/4/XAB; CNN: F49620-88-C-0129
Country of Publication:
United States
Language:
English