Existence of global solutions for isentropic gas flow with friction

In this paper, we study the existence of global entropy solutions for the Cauchy problem of the extended river flow system with a friction alpha(x) depending on the space variablex. First, under the boundedness of vertical bar alpha(x)vertical bar(L1(R))<i, we apply the viscosity-flux approximation method coupled with the maximum principle to obtain thea prioriL(infinity)estimates for the approximation solutions. Second, we prove the pointwise convergence of the approximation solutions by using the compactness framework from the compensated compactness theory. Finally, as a by-product, we obtain the existence of global solutions for isentropic gas flow in the Laval nozzle with friction.