2018/02/22 by Prasanta Kumar Barik, Barik, Prasanta Kumar, Ankik Kumar Giri +1
Engineering · Environmental Science · #34K30 #45G99 #45K05 #Analysis of PDEs (math.AP) #Coagulation and Flocculation Studies #Enhanced Oil Recovery Techniques #FOS: Mathematics #Minerals Flotation and Separation Techniques
paper · pdf · doi:10.48550/arxiv.1802.07961
openalex publication_date 2018/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An existence result on weak solutions to the continuous coagulation equation with collision-induced multiple fragmentation is established for certain classes of unbounded coagulation, collision and breakup kernels. In this model, a pair of particles can coagulate into a larger one if their confrontation is a completely inelastic collision; otherwise, one of them will split into many smaller particles due to a destructive collision. In the present work, both coagulation and fragmentation processes are considered to be intrinsically nonlinear. The breakup kernel may have a possibility to attain a singularity at the origin. The proof is based on the classical weak L1 compactness method applied to suitably chosen approximating equations. In addition, we study the uniqueness of weak solutions under additional growth conditions on collision and breakup kernels which mainly relies on the integrability of higher moments. Finally, it is obtained that the unique weak solution is mass-conserving.