Lifespan of classical discontinuous solutions to the generalized nonlinear initial–boundary Riemann problem for hyperbolic conservation laws with small BV data: Rarefaction waves

Abstract

In the present paper the author investigates the generalized nonlinear initial–boundary Riemann problem with small BV data for general n×n quasilinear hyperbolic systems of conservation laws with nonlinear boundary conditions in a half space {(t,x)|t≥0,x≥0}, where the Riemann solution contains rarefaction waves. Combining the techniques proposed by Li and Kong with the modified Glimm’s functional, the author obtains the almost global existence and lifespan of classical discontinuous solutions to a class of generalized nonlinear initial–boundary Riemann problem, which can be regarded as a small BV perturbation of the corresponding nonlinear initial–boundary Riemann problem. This result is also applied to the problem of planar steady supersonic Euler flow past a wedge.