Abstract:
We consider some boundary value problem describing the diffusion of thermal neutrons in a homogeneous one-dimensional medium accounting for absorption and breeding in the framework of a hyperbolic model of diffusion. We prove a unique existence theorem. The construction of a solution reduces to solving successively systems of linear integral equations of the second kind.
Keywords:generalized Fick's law, thermal neutrons, one-dimensional medium, Riemann matrices of the first and second kinds, reduction of a mixed problem to a Cauchy problem.