Existence and uniqueness of solutions for coagulation-fragmentation\n problems with singularity

2015/11/23 by Jitraj Saha, Jitendra Kumar, Saha, Jitraj +1
Environmental Science · Mathematics · #34A34 #45J05 #45L10 #Analysis of PDEs (math.AP) #Coagulation and Flocculation Studies #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1511.07115

openalex publication_date 2015/11/23 · openalex created_date 2022/08/28 · openalex updated_date 2026/07/28

Abstract

In this paper, existence and uniqueness of solutions to a non-linear, initial\nvalue problem is studied. In particular, we consider a special type of problem\nwhich physically represents the time evolution of particle number density\nresulted due to the coagulation and fragmentation process. The coagulation\nkernel is chosen from a huge class of functions, both singular and non-singular\nin nature. On the other hand, fragmentation kernel includes practically\nrelevant non-singular unbounded functions. Moreover, both the kernels satisfy a\nlinear growth rate of particles at infinity. The existence theorem includes\nlesser restrictions over the kernels as compared to the previous studies.\nFurthermore, strong convergence results on the sequence of functions are used\nto establish the existence theory.\n

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