Discrete Coagulation-Fragmentation equations with multiplicative coagulation kernel and constant fragmentation kernel

2024/09/26 by Jiwoong Jang, Jang, Jiwoong, Hung V. Tran +1 · 1 citation
Environmental Science · #Analysis of PDEs (math.AP) #Coagulation and Flocculation Studies #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2409.17974

openalex publication_date 2024/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Here, we study a discrete Coagulation-Fragmentation equation with a multiplicative coagulation kernel and a constant fragmentation kernel, which is critical. We apply the discrete Bernstein transform to the original Coagulation-Fragmentation equation to get two new singular Hamilton-Jacobi equations and use viscosity solution methods to analyze them. We obtain well-posedness, regularity, and long-time behaviors of the viscosity solutions to the Hamilton-Jacobi equations in certain ranges, which imply the well-posedness and long-time behaviors of mass-conserving solutions to the Coagulation-Fragmentation equation. The results obtained provide some definitive answers to a conjecture posed in [11,10], and are counterparts to those for the continuous case studied in [32].

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