Particle transport problems with general multiplying boundary conditions
Simona Mancini, Silvia Totaro · Transport Theory and Statistical Physics · 1998
We study the abstract version of an one-dimensional particle transport problem in a slab with general boundary conditions described by a linear positive operator A. We assume that particles can interact with the boundaries of the slab and multiply during the interaction. By using the theory of semigroups of operators, we prove existence uniqueness and positivity of the solution of this model. Moreover, we obtain, in two different ways, inequalities of physical interest for the number of particles in the slab at time t.