Large time behavior for a Hamilton–Jacobi equation in a critical coagulation-fragmentation model

@article{Mitake2020LargeTB,
  title={Large time behavior for a Hamilton–Jacobi equation in a critical coagulation-fragmentation model},
  author={Hiroyoshi Mitake and Hung V. Tran and Truong-Son Van},
  journal={arXiv: Analysis of PDEs},
  year={2020}
}
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 and constant fragmentation kernels. Our results include complete characterizations of stationary solutions and optimal conditions to guarantee large time convergence. In particular, we obtain convergence results under certain natural conditions on the initial data, and a nonconvergence result when… 
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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

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