On the Cauchy problem for macroscopic model of pedestrian flows

In this paper, we discuss the limit behavior of hyperbolic systems of conservation laws with stiff relaxation terms to the local systems as the relaxation time tends to zero. The prototype is crowd models derived from crowd dynamics according to macroscopic scaling when the flow of crowds is supposed to satisfy the paradigms of continuum mechanics. Under an appropriate structural stability condition, the asymptotic expansion is obtained when one assumes the existence of a smooth solution to the equilibrium system. In this case, the local existence of a classical solution is also shown.