Konarovskiy V. The system of interaction particles with variable weights

The thesis is dedicated to development of optimal order accuracy methods for solving wide classes of ill-posed problems. Dissertation is dedicated the system of interacting diffusion particles, which have mass, connected with the diffusion coefficient. Particles start from some finite or countable subset of real line and move independently up to the moment of the meeting, then particles coalesce and add their mass. Obtained processes describe the motion of interacting particles with variable mass. The case of random start is studied, when initial mass distribution of the particles is stationary. Asymptotic behaviour of a single particle is described. The Markov process, which define the system of diffusion particles with variable mass with singular interaction is described using martingale problem.