Abstract: In this paper, we study the Cauchy problem for a class of nonstrictly hyperbolic conservation laws which contain pressureless gas dynamics as a prototypical example. The Riemann solutions include two elementary waves: delta-wave and contact discontinuity. By studying the interaction of these elementary waves and employing improved generalized characteristics approach, we establish the convergence of approximate solutions constructed by piecing together all Riemann solutions, and prove the global existence of measure-value solution to the Cauchy problem. Moreover, the singular set of solution consists of at most denumerable Lipschitz continuous curves.
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