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The discrete unbounded coagulation-fragmentation equation with growth, decay and sedimentation

  • * Corresponding author: J. Banasiak

    * Corresponding author: J. Banasiak 
The research was supported by the NRF grants N00317 and N102275, and the National Science Centre, Poland, grant 2017/25/B /ST1/00051.
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  • In this paper we study the discrete coagulation–fragmentation models with growth, decay and sedimentation. We demonstrate the existence and uniqueness of classical global solutions provided the linear processes are sufficiently strong. This paper extends several previous results both by considering a more general model and and also signnificantly weakening the assumptions. Theoretical conclusions are supported by numerical simulations.

    Mathematics Subject Classification: 34G20, 47D05, 47H07, 47H14, 47H20, 65J15, 82D, 70F45, 92D25.

    Citation:

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  • Figure 1.  Evolution of the pure coagulation-fragmentation model (2) with the coagulation kernel (39a) and the fragmentation kernel (38a): number of clusters $ u_n(t) $ (top left); distribution of cluster masses $ nu_n(t) $ (top right); the total number of particles (middle left); the total mass (middle right) and the higher order moments (bottom)

    Figure 2.  Evolution of the pure coagulation-fragmentation model (2) with the coagulation kernel (39b) and the fragmentation kernel (38b): number of clusters $ u_n(t) $ (top left); distribution of cluster masses $ nu_n(t) $ (top right); the total number of particles (middle left); the total mass (middle right) and the higher order moments (bottom)

    Figure 3.  Evolution of the growth-decay-coagulation-fragmentation model (2) with the coagulation kernel (39a) and the fragmentation kernel (38a): number of clusters $ u_n(t) $ (top left); distribution of cluster masses $ nu_n(t) $ (top right); the total number of particles (middle left); the total mass (middle right) and the higher order moments (bottom)

    Figure 4.  Evolution of the growth-decay-coagulation-fragmentation model (2) with the coagulation kernel (39b) and the fragmentation kernel (38b): number of clusters $ u_n(t) $ (top left); distribution of cluster masses $ nu_n(t) $ (top right); the total number of particles (middle left); the total mass (middle right) and the higher order moments (bottom)

    Figure 5.  Evolution of the decay-sedimentation-coagulation-fragmentation model (2) with the coagulation kernel (39a) and the fragmentation kernel (38a): number of clusters $ u_n(t) $ (top left); distribution of cluster masses $ nu_n(t) $ (top right); the total number of particles (bottom left) and the total mass (bottom right)

    Figure 6.  Evolution of the decay-sedimentation-coagulation-fragmentation model (2) with the coagulation kernel (39b) and the fragmentation kernel (38b): number of clusters $ u_n(t) $ (top left); distribution of cluster masses $ nu_n(t) $ (top right); the total number of particles (bottom left) and the total mass (bottom right)

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