Global existence to the discrete Safronov-Dubovskiǐ coagulation equations and failure of mass-conservation

This paper presents the existence of global solutions to the discrete Safronov-Dubvoskiǐ coagulation equations for a large class of coagulation kernels satisfying $Λ_{i,j} = θ_i θ_j + κ_{i,j}$ with $κ_{i,j} \leq Aθ_i θ_j, \ \ \forall \ \ i,j\ge 1$ where the sequence $(θ_i)_{i\geq 1}$ grows linearly or superlinearly with respect to $i$. Moreover, the failure of mass-conservation of the solution is also addressed which confirms the occurrence of the gelation phenomenon.

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