Transport equations with boundary conditions of reverse reflection type

A study is performed of transport equations on arbitrary three‐dimensional domains with boundary conditions of reverse reflection type. The existence of the dominant eigenvalue of the criticality problem is proved and its independence of the functional setting and its continuous dependence on a variety of data are established. The corresponding time‐dependent problem is shown to be well‐posed, also for a conservative boundary. The relationship between the criticality and the time‐dependent problem is given explicitly.