Almost global existence of classical discontinuous solutions to genuinely nonlinear hyperbolic systems of conservation laws with small BV initial data

In the present paper, the author investigates the initial problem for genuinely nonlinear quasilinear hyperbolic systems of conservation laws under small BV perturbations of the Riemann initial data, where 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 and Kong with the modified Glimmʼs functional, the author obtains the almost global existence and lifespan of classical discontinuous solutions to the above problem. This result is also applied to the system of one-dimensional isentropic flow.