The existence and uniqueness of global classical solutions to the Safronov-Dubovskii coagulation equation are established for the coagulation kernels satisfying the linear growth condition i.e. γ i,j ≤ A(i δ + j δ ) for some δ ∈ [0, 1] which extends the results obtained in [6]. In particular, the initial condition may have an infinite second moment as long as δ < 1. Moreover, the solution constructed herein is shown to be mass-conserving. In the end, the continuous dependence on the initial data and the large-time behaviour of solutions are also addressed.

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In this article, the existence of global classical solutions to the discrete coagulation equations with collisional breakage is established for collisional kernel having linear growth whereas the uniqueness is shown under additional restrictions on collisional kernel. Moreover, mass conservation property and propagation of moments of solutions are also discussed.

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This paper presents the existence of global solutions to the discrete Safronov-Dubvoski ǐ coagulation equations for a large class of coagulation kernels satisfying Λ i,j = θ i θ j + κ i,j with κ i,j ≤ Aθ i θ j , ∀ i, j ≥ 1 where the sequence (θ i ) i≥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.