  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.
