Abstract
each Kn(f) being derived from an n-linear operator by equating the argument functions. Equations of type (1) occur in physics, especially in connection with transport phenomena and kinetic theory. In this context the summands Kn(f) in (2) possess a simple interpretation: for n > 2 Kn(f) is the contribution toward the time-rate of reshuffling of a distribution f(x, t), due to n-tuple collisions, n-fold coalescences or similar processes, while Ki(f) is the contribution due to breakup or other destructive process. For further details about this, and other background material, see [1; 2] and [3]. Our main result is a theorem asserting unique local existence of solutions of Equation (1). These are obtained by the Picard iterative method and bounds on various approximation errors are given or can be developed. However, these estimates seem to be too crude for actual computation.
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