Local mass-conserving solution for a critical coagulation-fragmentation equation

The critical coagulation-fragmentation equation with multiplicative coagulation and constant fragmentation kernels is known to not have global mass-conserving solutions when the initial mass is greater than 1. We show that for any given positive initial mass with finite second moment, there is a tim...

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Bibliographic Details
Published in:Journal of Differential Equations 2023-04, Vol.351, p.49-62
Main Authors: Tran, Hung V., Van, Truong-Son
Format: Article
Language:English
Subjects:
Bernstein transform
Critical coagulation-fragmentation equations
Local well-posedness
Singular Hamilton-Jacobi equations
Viscosity solutions
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Summary:The critical coagulation-fragmentation equation with multiplicative coagulation and constant fragmentation kernels is known to not have global mass-conserving solutions when the initial mass is greater than 1. We show that for any given positive initial mass with finite second moment, there is a time T⁎>0 such that the equation possesses a unique mass-conserving solution up to T⁎. The novel idea is to singularly perturb the constant fragmentation kernel by small additive terms and study the limiting behavior of the solutions of the perturbed system via the Bernstein transform.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2022.12.015