Bounds and Maximum Principles for the Solution of the Linear Transport Equation
Edward W. Larsen · SIAM Journal on Mathematical Analysis · 1981
Pointwise bounds are derived for the solution of time-independent linear transport problems with surface sources in convex spatial domains. Under specified conditions, upper bounds are derived which, as a function of position, decrease with distance from the boundary. Under other conditions, lower bounds are derived which increase with distance from the boundary. Also, sufficient conditions are obtained for the existence of maximum and minimum principles, and a counterexample is given which shows that such principles do not always exist.