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Admissibility and uniqueness of weak solutions to hyperbolic systems of balance laws

✍ Scribed by Witold Kosiński; B. Brosowski

Publisher
John Wiley and Sons
Year
1989
Tongue
English
Weight
836 KB
Volume
11
Category
Article
ISSN
0170-4214

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✦ Synopsis

Communicated by B. Brosowski

A system of quasi-linear fint-order equations written in the divergence form and constrained by the unilateral differential inequality (the second law of thermodynamics) with a strictly m m v e entropy function is analysed. In the class BV, i.e. a subset of regular distributions represented by functions of bounded variation in the sense of Tonelli-Cesari, a weak solution to the system is defined. The parabolized version of the system is also discussed in order to define an admissible weak solution as a limit of a sequence of Lipschitz continuous solutions to the parabolic problem. It is proved that an admissible weak solution of the Cauchy problem is unique in the class BV.

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