Work

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

Year: 2025

Type: article

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 (Escobedo et al. in Commun. Math. Phys. 231(1): 157–188, 2002 ; Escobedo et al. in J. Differ. Equ. 195(1): 143–174, 2003 ) and are counterparts to those for the continuous case studied in (Tran and Van in Commun. Pure Appl. Math. 75(6):1292–1331, 2022 ).

Source: Advances in Continuous and Discrete Models

DOI: 10.1186/s13662-025-03946-4

Authors: Jiwoong Jang, Hung Vinh Tran

Institutions: University of Maryland, College Park, University of Wisconsin–Madison

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $1,890

Funder: National Science Foundation