A MATHEMATICAL-MODEL FOR PARTICLE-TRANSPORT WITH MOLLIFIED BOUNDARY-CONDITIONS

We consider a mathematical model of the particle streaming phenomenon in plane geometry, which may be of interest in gas kinetic theory as well as in several applications. We show that the streaming operator T0f = -vy partial derivative-f partial derivative-x, f is-an-element-of X1 = L1[(-a, + a) x (-1, + 1)], subject to a mollified type of Maxwell's boundary conditions, generates a strongly continuous semigroup {exp(tT0), t greater-than-or-equal-to 0} even if the boundary walls at x = -a and at x = +a are particle multiplying. Such a result can be used to study linear and nonlinear evolution problems of particle transport, under the assumption that a container has walls which reflect, absorb or multiply the impinging particles.