The fragmentation equation with size diffusion: Well posedness and long-term behaviour

被引:1
作者
Laurencot, Ph [1 ]
Walker, Ch [2 ]
机构
[1] Univ Toulouse, CNRS, UMR 5219, Inst Math Toulouse, F-31062 Toulouse 9, France
[2] Leibniz Univ Hannover, Inst Angew Math, Welfengarten 1, D-30167 Hannover, Germany
关键词
Fragmentation; size diffusion; well posedness; convergence; semigroup; perturbation; KINETICS; DYNAMICS;
D O I
10.1017/S0956792521000346
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The dynamics of the fragmentation equation with size diffusion is investigated when the size ranges in (0, infinity). The associated linear operator involves three terms and can be seen as a nonlocal perturbation of a Schrodinger operator. A Miyadera perturbation argument is used to prove that it is the generator of a positive, analytic semigroup on a weighted L-1-space. Moreover, if the overall fragmentation rate does not vanish at infinity, then there is a unique stationary solution with given mass. Assuming further that the overall fragmentation rate diverges to infinity for large sizes implies the immediate compactness of the semigroup and that it eventually stabilizes at an exponential rate to a one-dimensional projection carrying the information of the mass of the initial value.
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页码:1083 / 1116
页数:34
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