Globally Smooth Solutions to an Inhomogeneous Quasilinear Hyperbolic System Arising in Chemical Engineering

In this paper we have obtained the existence of globally smooth solutions to an inhomogeneous nonstrictly hyperbolic system u_t - (v(1 - u))_x = 0, v_t + (frac{1}{2}v² - c_0u)_x = f(u,v) by employing the characteristic method and the fixedpoint theorem in Banach spaces.