Radially symmetric solutions for a class of hyperbolic systems of conservation laws (Q1365531)

The author studies theoretically a class of hyperbolic conservation laws in two space dimensions, which includes the Weyl equation of relativistic quantum mechanics and the complex Burgers' equation as prototypes. He derives a class of radially symmetric solutions. These solutions are multiple valued, which has a physical interpretation in case of the Weyl equation. Moreover, symmetric solutions corresponding to the one-dimensional inviscid Burgers' equation can be used to validate numerical algorithms for multi-dimensional systems of conservation laws. The study of solutions of particular classes of hyperbolic conservation laws is important since so far no general existence theorem for weak solutions of nonstrictly hyperbolic conservation laws has been established.