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A continuum individual-based model of hopping and coalescing particles is introduced and studied. Its microscopic dynamics are described by a hierarchy of evolution equations obtained in the paper. Then the passage from the micro- to mesoscopic dynamics is performed by means of a Vlasov-type scaling. The existence and uniqueness of solutions of the corresponding kinetic equation are proved.
The aim of this paper is to discuss a special case of a coalescing random jumps model of infinitely many jumping individuals. Jumps are embedded with repulsion at the target point and coalescence kernel is defined in such a way that for two coalescing individuals the result is deterministically defined. A possible approach to study the dynamics of the system numerically is discussed. It is based on a Poisson approximation of states of the system. Some interesting results of simulations are showed....
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