Existence of global LpLp solutions to a symmetric system of Keyfitz–Kranzer type

In this paper, we give the global existence of LpLp bounded entropy solutions for the Cauchy problem of a symmetric system of Keyfitz–Kranzer type. The main difficulty lies in establishing the LpLp estimate of the viscosity solutions because the initial data may not be L∞L∞ bounded and the principle of invariant regions developed by Conley–Chuey–Smoller is invalid here. We obtain the existence of the global weak solutions using the compensated compactness method and BV estimates on viscosity solutions.