Time Asymptotics for a Critical Case in Fragmentation and Growth-Fragmentation Equations

@article{Doumic2015TimeAF,
  title={Time Asymptotics for a Critical Case in Fragmentation and Growth-Fragmentation Equations},
  author={Marie Doumic and Miguel Escobedo},
  journal={CoRR},
  year={2015},
  volume={abs/1510.03588}
}
Fragmentation and growth-fragmentation equations is a family of problems with varied and wide applications. This paper is devoted to the description of the long-time asymptotics of two critical cases of these equations, when the division rate is constant and the growth rate is linear or zero. The study of these cases may be reduced to the study of the following fragmentation equation: ∂ ∂t u(t, x) + u(t, x) = ∞ ∫ x k0 ( x y ) u(t, y)dy. Using the Mellin transform of the equation, we determine… CONTINUE READING
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