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

2022/07/08 by Mashkoor Ali, Ali, Mashkoor, Ankik Kumar Giri +1
Mathematics · Medicine · #34A12 #34K30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2207.12094

openalex publication_date 2022/07/08 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

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 ≤ 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.

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