  The paper is devoted to constructing the global solutions around global
Maxwellians to the initial-boundary value problem on the Boltzmann equation in
general bounded domains with isothermal diffuse reflection boundaries. We allow
a class of non-negative initial data which have arbitrary large amplitude and
even contain vacuum. The result shows that the oscillation of solutions away
from global Maxwellians becomes small after some positive time provided that
they are initially close to each other in $L^2$. This yields the disappearance
of any initial vacuum and the exponential convergence of large-amplitude
solutions to equilibrium in large time. The isothermal diffuse reflection
boundary condition plays a vital role in the analysis. The most key ingredients
in our strategy of the proof include: (i)
$L^2_{x,v}$--$L^\infty_xL^1_v$--$L^\infty_{x,v}$ estimates along a bootstrap
argument; (ii) Pointwise estimates on the upper bound of the gain term by the
product of $L^\infty$ norm and $L^2$ norm; (iii) An iterative procedure on the
nonlinear term.
