Abstract
A class of nonlinear integro-differential evolution problems arising in space-independent particle-transport theory is studied for the case of general speed dependence of the collision frequencies. A decomposition of the high nonlinearity associated with this class of problems, and a classification of the relevant solution for the distribution function, are attempted via a systematic reference to the continuity equation for the total density of the particles considered, and to other additional algorithms. Different cases of plausible behaviors for the cross sections are then examined. Some generalizations of the continuity equation so obtained are, finally, discussed with comparison also made to the simple form holding in the case of 1/v cross sections.
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