  We numerically solve the transport equations for a quark gas described by the
the Nambu-Jona-Lasinio model. The mean field equations of motion, which consist
of the Vlasov equation for the density and the gap equation for the mean field,
are discussed, and energy and momentum conservation are proven. Numerical
solutions of the partial differential equations are obtained by applying finite
difference methods. For an expanding fireball of the light quark mass evolves
from small values initially to the value of 350 MeV. This leads to a depletion
of the high energy part of the quark spectrum and an enhancement at low
momenta. When collisions are included one obtains an equation of the Boltzmann
type, where the transition amplitudes depend on the properties of the medium.
These equations are given for flavor SU(3), i. e. including strangeness. They
are solved numerically in the relaxation time approximation and the time
evolution of various observables is given. Medium effects in the relaxtion
times do not significantly influence the shape of the spectra. The mass of the
strange quark changes little during the expansion. The strangeness yield and
the slope temperatures of the final spectra are studied as a function of the
size of the initial fireball.
