Coagulation‐Fragmentation Equations with Multiplicative Coagulation Kernel and Constant Fragmentation Kernel

We study a critical case of coagulation‐fragmentation equations with multiplicative coagulation kernel and constant fragmentation kernel. Our method is based on the study of viscosity solutions to a new singular Hamilton‐Jacobi equation, which results from applying the Bernstein transform to the ori...

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Bibliographic Details
Published in:Communications on pure and applied mathematics 2022-06, Vol.75 (6), p.1292-1331
Main Authors: Tran, Hung V., Van, Truong‐Son
Format: Article
Language:English
Subjects:
Coagulation
Fragmentation
Kernels
Mathematical analysis
Viscosity
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Summary:We study a critical case of coagulation‐fragmentation equations with multiplicative coagulation kernel and constant fragmentation kernel. Our method is based on the study of viscosity solutions to a new singular Hamilton‐Jacobi equation, which results from applying the Bernstein transform to the original coagulation‐fragmentation equation. Our results include well‐posedness, regularity, and long‐time behaviors of viscosity solutions to the Hamilton‐Jacobi equation in certain regimes, which have implications to well‐posedness and long‐time behaviors of mass‐conserving solutions to the coagulation‐fragmentation equation. © 2021 Wiley Periodicals LLC.
ISSN:0010-3640
1097-0312
DOI:10.1002/cpa.21979