On the two-component Hunter–Saxton system
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In 1991 Hunter and Saxton introduced a novel equation related to the dynamics of liquid crystals. The equation exhibited startling properties, among them wave breaking in finite time. Here we study the effects of wave breaking on a two-component system generalizing the equation by Hunter and Saxton. In particular we establish global existence of different classes of weak solutions, and examine their stability. Much effort has been devoted to understanding traffic flow. We find a solution of a Riemann problem for a particular model of traffic flow at an intersection, and find a special limit Riemann solver when the maximal queue size tends to zero.