Propagation of weak discontinuities for quasilinear hyperbolic systems with coefficients functionally dependent on solutions

The propagation of weak discontinuities for quasilinear systems with coefficients functionally dependent on the solution is studied. We demonstrate that, similarly to the case of usual quasilinear systems, the transport equation for the intensity of weak discontinuity is quadratic in this intensity. However, the contribution from the (nonlocal) functional dependence appears to be in principle linear in the jump intensity (with some exceptions). For illustration, several examples, including two hyperbolic systems (with functional dependence), the dispersive Maxwell equations and fluid equations of the Hall plasma thruster, are considered.