  This paper is concerned with the Boltzmann equation with specular reflection
boundary condition. We construct a unique global solution and obtain its large
time asymptotic behavior in the case that the initial data is close enough to a
radially symmetric homogeneous datum. The result extends the case of Cauchy
problem considered by Arkeryd-Esposito-Pulvirenti [Comm. Math. Phys. 111(3):
393-407 (1987)] to the specular reflection boundary value problem in bounded
domain.
