Abstract
A general system of quasi-linear first order equations written in the divergence form and constrained by a differential inequality (the second law of thermodynamics) is analysed. Compatibility conditions are presented. In the BV-space, which is a subspace of those regular distributions that are represented by functions of bounded variation, a weak solution to the system is defined. In the proposed definition, written as a kind of a variational inequality, the system of equations and the thermodynamic admissibility condition are accommodated. The application of this concept in the investigation of uniqueness of an admissible weak solution to a Cauchy problem in the BV-space is shortly presented.
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