Extensions of hyperbolic systems of balance laws (Q2501871)

In this paper, hyperbolic systems of PDEs are considered. An algorithm to extend a hyperbolic system of balance laws to a system of higher dimension is presented. The extended system is such that the set of admissible weak solutions of the initial system is isomorphic to a subset of admissible weak solutions of the extended one. In addition, the extended system inherits hyperbolicity and symmetry group of the initial system. Some properties of the characteristic speeds of the extended system is founded. The construction of mathematically attractive new model of two-fluid flow is obtained as an application of this algorithm.