  For the Boltzmann equation with cutoff hard potentials, we construct the
unique global solution converging with an exponential rate in large time to
global Maxwellians not only for the specular reflection boundary condition with
the bounded convex C^3 domain but also for a class of large amplitude initial
data where the L^infty norm with a suitable velocity weight can be arbitrarily
large but the relative entropy need to be small. A key point in the proof is to
introduce a delicate nonlinear iterative process of estimating the gain term
basing on the triple Duhamel iteration along the linearized dynamics.
