Existence of global Lp solutions to a symmetric system of Keyfitz-Kranzer type

Abstract In this paper, we give the global existence of L p bounded entropy solutions for the Cauchy problem of a symmetric system of Keyfitz–Kranzer type. The main difficulty lies in establishing the L p estimate of the viscosity solutions because the initial data may not be 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.