Lifespan of classical discontinuous solutions to general quasilinear hyperbolic systems of conservation laws with small BV initial data: Rarefaction waves

Abstract

In the present paper the author investigates the global structure stability of Riemann solutions for general quasilinear hyperbolic systems of conservation laws under small BV perturbations of the initial data, where the Riemann solution contains rarefaction waves, while the perturbations are in BV but they are assumed to be C1-smooth, with bounded and possibly large C1-norms. Combining the techniques employed by Li–Kong with the modified Glimm’s functional, the author obtains a lower bound of the lifespan of the piecewise C1 solution to a class of generalized Riemann problems, which can be regarded as a small BV perturbation of the corresponding Riemann problem. This result is also applied to the system of traffic flow on a road network using the Aw–Rascle model.