  This work deals with the inhomogeneous Landau equation on the torus in the
cases of hard, maxwellian and moderately soft potentials. We first investigate
the linearized equation and we prove exponential decay estimates for the
associated semigroup. We then turn to the nonlinear equation and we use the
linearized semigroup decay in order to construct solutions in a
close-to-equilibrium setting. Finally, we prove a exponential stability for
such a solution, with a rate as close as we want to the optimal rate given by
the semigroup decay.
