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

@article{Tran2021CoagulationFragmentationEW,
  title={Coagulation‐Fragmentation Equations with Multiplicative Coagulation Kernel and Constant Fragmentation Kernel},
  author={Hung V. Tran and Truong-Son Van},
  journal={Communications on Pure and Applied Mathematics},
  year={2021},
  volume={75}
}
  • H. Tran, Truong-Son Van
  • Published 29 October 2019
  • Mathematics
  • Communications on Pure and Applied Mathematics
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… 
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
Large time behavior for a Hamilton–Jacobi equation in a critical coagulation-fragmentation model
We study the large time behavior of the sublinear viscosity solution to a singular Hamilton-Jacobi equation that appears in a critical Coagulation-Fragmentation model with multiplicative coagulation

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