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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 $$\partial C(x,t)/\partial t=\dfrac{1}{2}\int^x_0 dy\,K(y,x-y)C(x-y,t)-C(x,t)\int^{\infty}_o dy\,K(x,y)C(y,t)+\partial[m(x)C(x,t)]/\partial x$$ 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
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