We construct a modified Arratia flow with mass and energy conservation. We
suppose that particles have a mass obeying the conservation law, and their
diffusion is inversely proportional to the mass. Our main result asserts that
such a system exists under the assumption of the uniform mass distribution on
an interval at the starting moment. We introduce a stochastic integral with
respect to such a flow and obtain the total local time as the density of the
occupation measure for all particles.Comment: 47 page
We study asymptotic properties of the system of interacting diffusion
particles on the real line which transfer a mass [arXiv:1408.0628]. The system
is a natural generalization of the coalescing Brownian motions. The main
difference is that diffusion particles coalesce summing their mass and changing
their diffusion rate inversely proportional to the mass. First we construct the
system in the case where the initial mass distribution has the moment of the
order greater then two as an $L_2$-valued martingale with a suitable quadratic
variation. Then we find the relationship between the asymptotic behavior of the
particles and local properties of the mass distribution at the initial time
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