MATHEMATICAL THEORY ON THE DISCRETE COLLISION-INDUCED BREAKAGE EQUATIONS AND THE SAFRONOV-DUBVOSKIǏ COAGULATION EQUATIONS

Abstract

The scientific interest of this thesis lies in investigating and analyzing discrete nonlinear breakage models and the discrete Safronov–Dubovskiˇi coagulation model. The thesis is divided into two parts, with the first part focusing on the nonlinear breakage equations and the second part dedicated to the discrete Safronov–Dubovskiˇi coagulation equations. In the first part, the thesis establishes the existence of mass-conserving weak solutions to the discrete nonlinear breakage equations. This is achieved by utilizing a weak compactness technique. The analysis expands on previous work by relaxing the growth conditions on the collision kernel and the daughter distribution function, providing a more comprehensive understanding of the system when coagulation is turned off. The thesis thoroughly examines the scenario where there is no mass transfer during collisions and investigates the nonlinear breakage equations under this condition. Additionally, the thesis considers the nonlinear breakage equations allowing mass transfer during collisions and proves the well-posedness of the solution using moment estimates. The existence of stationary solutions is also demonstrated.