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The solution of nonlinear coagulation problem with mass loss. (English) Zbl 1101.82018

The authors consider the following integro-differential equation

C(x,t)/t=1 2 0 x dyK(y,x-y)C(x-y,t)-C(x,t) o dyK(x,y)C(y,t)+[m(x)C(x,t)]/x

reporting the evolution of the size distribution function C(x,t) of a system of particles undergoing coalescence (K(x,y) is the coalescence kernel) and mass loss (m(x) is the main loss rate, depending on the size x). They consider the special case m(x)=mx, and two kinds of kernels: K=1,K=xy. For each of these cases problems with different initial conditions are formulated and approximate solutions are found by means of two different iterative methods: the method of He and the decomposition method of Adomian, both briefly sketched in the paper.

MSC:
82C22Interacting particle systems
Keywords:
Coagulation