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This paper presents the existence of global solutions to the discreteSafronov-Dubvoski\v{i} coagulation equations for a large class of coagulationkernels satisfying $\Lambda_{i,j} = \theta_i \theta_j + \kappa_{i,j}$ with$\kappa_{i,j} \leq A\theta_i \theta_j, \ \ \forall \ \ i,j\ge 1$ where thesequence $(\theta_i)_{i\geq 1}$ grows linearly or superlinearly with respect to$i$. Moreover, the failure of mass-conservation of the solution is alsoaddressed which confirms the occurrence of the gelation phenomenon.

Global existence to the discrete Safronov-Dubovski\v{i} coagulation equations and failure of mass-conservation