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Existence and uniqueness of steady-state solution to a singular coagulation–fragmentation equation
Journal of Computational and Applied Mathematics ( IF 1.883 ) Pub Date : 2020-05-21 , DOI: 10.1016/j.cam.2020.112992
Debdulal Ghosh; Jitraj Saha; Jitendra Kumar

In this article, we prove the existence of an equilibrium solution to the coagulation–fragmentation equation with • [(i)] a singular coagulation kernel in the form K(x,y)=(1+xλ+yλ)(xy)σ,where σ∈0,12 and λ−σ∈[0,1], and • [(ii)] a fragmentation kernel in the form F(x,y)=b0+b(x+y)m,where b0>0 and b,m≥0. Importantly, in the entire study, the detailed balance condition is not assumed. It is shown that the equilibrium solution of the problem under consideration is unique in the space of all continuous functions on (0,∞). The proposed results are demonstrated by a numerical illustration.
更新日期:2020-05-21

 

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