Well-posedness to the discrete collision-induced breakage equation and various properties of solutions

2022/09/30 by Mashkoor Ali, Ali, Mashkoor, Ankik Kumar Giri +2
Mathematics · Physics and Astronomy · #34A12 #34K30 #46B50 #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2209.15411

openalex publication_date 2022/09/30 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

A discrete version of the nonlinear collision-induced breakage equation is studied. Existence of solutions is investigated for a broad class of unbounded collision kernels and daughter distribution functions, the collision kernel a_i,j satisfiying a_i,j ≤ A i j for some A>0. More precisely, it is proved that given suitable conditions, there exists at least one mass-conserving solution for all times. A result on the uniqueness of solutions is also demonstrated under reasonably general conditions. Furthermore, the propagation of moments, differentiability, and the continuous dependence of solutions are established, along with some invariance properties and the large-time behaviour of solutions.

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