Steady and self-similar solutions of non-strictly hyperbolic systems of conservation laws

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We consider solutions of two-dimensional m × m systems hyperbolic conservation laws that are constant in time and along rays starting at the origin. The solutions are assumed to be small L∞ perturbations of a constant state and entropy admissible, and the system is assumed to be non-strictly hyperbolic with eigenvalues of constant multiplicity. We show that such a solution, initially assumed bounded, must be a special function of bounded variation, and we determine the possible configuration of waves. As a corollary, we extend some regularity and uniqueness results for some one-dimensional Riemann problems.