Conservation laws for 2 × 2 hyperbolic systems

In this paper we determine classes of conservation laws admitted by 2 × 2 first-order hyperbolic nonhomogeneous systems by following the so-called direct method proposed by Bluman et al. Such mathematical models can describe several situations of interest in applications like isentropic fluid dynamics, viscoelastic media, traffic flows, and transmission lines. A full classification of all the possible local conservation laws is given in the case where the governing equations are homogeneous. The general results obtained have been used in two examples concerning the p-system and a 2 × 2 model describing transmission lines.