In this paper, we extend the result in [16] to general p(v). We prove that, under condition (M) when p≥3/2, where , there exists a unique global continuous solution to the Riemann problem (E), (R), whose structure is similar to the local solution. When 1P_*≤P~*5/4, or P_*=P~*=5/4, or 5/4P_*≤P~*3/2, where P_*=inf P and P~*=sup P for all u under consideration, if at least one of the initial centered rarefaction waves is sufficiently strong, then the solution must be breakdown in a finite
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