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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:
 82C22 Interacting particle systems in time-dependent statistical mechanics
Coagulation
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