  A model kinetic equation is solved exactly for a special stationary state
describing nonlinear Couette flow in a low density system of inelastic spheres.
The hydrodynamic fields, heat and momentum fluxes, and the phase space
distribution function are determined explicitly. The results apply for
conditions such that viscous heating dominates collisional cooling, including
large gradients far from the reference homogeneous cooling state. Explicit
expressions for the generalized transport coefficients (e.g., viscosity and
thermal conductivity) are obtained as nonlinear functions of the coefficient of
normal restitution and the shear rate.These exact results for the model kinetic
equation are also shown to be good approximations to the corresponding state
for the Boltzmann equation via comparison with direct Monte Carlo simulation
for the latter
