Abstract: In this article, we study the global L^∞ entropy solutions for the Cauchy problem of system of isentropic gas dynamics in a divergent nozzle with a friction. Especially when the adiabatic exponent γ=3, we apply for the maximum principle to obtain the L^∞ estimates w(ρ^δ,ε, u^δ,ε) ≤ B(t) and z(ρ^δ,ε, u^δ,ε) ≤ B(t) for the viscosity solutions (ρ^δ,ε, u^δ,ε), where B(t) is a nonnegative bounded function for any finite time t. This work, in the special case γ ≥ 3, extends the previous works, which provided the global entropy solutions for the same Cauchy problem with the restriction w(ρ^δ,ε, u^δ,ε) ≤ 0 or z(ρ^δ,ε, u^δ,ε) ≤ 0.

Key words: global L^∞ solution, isentropic gas dynamics, source terms, flux approximation, compensated compactness