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

  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},
  • 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… 
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