ABSTRACT. In this paper a numerical method is proposed for obtaining stable solutions to the initialvalue problem for the pair of conservation laws Ut + (jU j2U)x = 0 (0.1) where U 2 IR2. These equations constitute a standard model describing small amplitude plane wave solutions to rotationally invariant PDE systems arising in continuum mechanics. In particular, viscous regularization of (0.1) by fflUxx is not uniform as ffl! 0. Therefore finite difference schemes which include numerical dissipation of this type fail to approximate certain of the dynamically stable weak solutions of the inviscid system (0.1). Our proposal is to extend the system and solve the triple of conservation laws rt + (r3)x = 0 Ut + (r2U)x = 0 (0.2
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