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

Abstract

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.