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The global existence of mass-conserving weak solutions to theSafronov-Dubovskii coagulation equation is shown for the coagulation kernelssatisfying the at most linear growth for large sizes. In contrast to previousworks, the proof mainly relies on the de la Vallee-Poussin theorem [8, Theorem7.1.6], which only requires the finiteness of the first moment of the initialcondition. By showing the necessary regularity of solutions, it is shown thatthe weak solutions con-structed herein are indeed classical solutions. Underadditional restrictions on the initial data, the uniqueness of solutions isalso shown. Finally, the continuous dependence on the initial data and thelarge-time behaviour of solutions are also addressed.

On the discrete Safronov-Dubovskii coagulation equation: well-posedness, mass-conservation and asymptotic behaviour