Neutron Transport in a Slab with Moving Boundaries
Aldo Belleni‐Morante, R. Farano · SIAM Journal on Applied Mathematics · 1976
We study a monoenergetic neutron transport initial value problem in a nonhomogeneous slab with time-dependent half-thickness. By using the theory of semigroups, we prove the existence of a unique positive solution $u = u( t )$ belonging to the Hilbert space of square summable functions. We also investigate some properties of $\| {u( t )} \|$ which are of practical interest. Finally, we briefly examine the case in which the initial value problem under consideration admits only a mild solution.