Coagulation-Fragmentation equations with multiplicative coagulation\n kernel and constant fragmentation kernel

2019/10/29 by Hung V. Tran, Tran, Hung V., Truong‐Son Van +1
Mathematics · #35B65 #35F21 #35Q99 #44A10 #45J05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1910.13424

openalex publication_date 2019/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a critical case of Coagulation-Fragmentation equations with\nmultiplicative coagulation kernel and constant fragmentation kernel. Our method\nis based on the study of viscosity solutions to a new singular Hamilton-Jacobi\nequation, which results from applying the Bernstein transform to the original\nCoagulation-Fragmentation equation. Our results include wellposedness,\nregularity and long-time behaviors of viscosity solutions to the\nHamilton-Jacobi equation in certain regimes, which have implications to\nwellposedness and long-time behaviors of \mass-conserving solutions to\nthe Coagulation-Fragmentation equation.\n

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