Global Solutions to the Discrete Nonlinear Breakage Equations without Mass Transfer

2025/07/09 by Mashkoor Ali, Ali, Mashkoor, Philippe Laurençot +1
Mathematics · Medicine · Physics and Astronomy · #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2507.06685

openalex publication_date 2025/07/09 · openalex created_date 2025/10/09 · openalex updated_date 2026/07/28

Abstract

Global existence of mild solutions to the discrete collisional breakage equations is established for a broad class of collision kernels, without imposing any growth assumptions. In addition, classical solutions are constructed, and uniqueness is proved for an appropriate class of kinetic coefficients and initial data. The large time behavior of solutions is also discussed, and numerical simulations are presented to support the theoretical results.

Citations

• Mass-conserving weak solutions to the continuous nonlinear fragmentation equation in the presence of mass transfer
• Existence and Non-existence for Exchange-Driven Growth Model
• The Redner-ben-Avraham-Kahng cluster system without growth condition on the kinetic coefficients
• The discrete generalized exchange-driven system
• The continuous collision-induced nonlinear fragmentation equation with non-integrable fragment daughter distributions
• The discrete collision-induced breakage equation with mass transfer: well-posedness and stationary solutions
• Global classical solutions to the continuous coagulation equation with\n collisional breakage
• Weak solutions to the continuous coagulation model with collisional\n breakage
• Shattering transitions in collision-induced fragmentation

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• Weak convergence analysis for non-linear collisional induced breakage equation with singular kernel
• Mass conserving global solutions for the nonlinear collision-induced fragmentation model with a singular kernel