Asymptotics of the solution to the mixed problem for the kinetic equation of neutron transport (Q1363981)

The asymptotic behaviour of the kinetic equation of neutron transport is considered. The coefficient \(\sigma(v,r)\) (the collision probability per unit of the path length) depends on the neutron velocity \(v\) and the space variable \(r\in D\). The asymptotics of the solution is analysed on the small parameter \(h=(\sigma_0 d)^{-1}\), where \(\sigma_0= \min\sigma(v,r)\), \(d=\text{diam}(D)\). This problem is divided into two cases: the coefficients of equation change smoothly (fluently) or they are rapidly oscillating. The conditions of the main results are expressed by the spectrum of the operator-valued symbol of the modified kinetic equation operator. Then the resolvent of that operator tends to zero, when special conditions are fulfilled.