Smoluchowski’s discrete coagulation equation with forcing

  • Christian Kuehn
  • Sebastian ThromEmail author


In this article we study an extension of Smoluchowski’s discrete coagulation equation, where particle in- and output takes place. This model is frequently used to describe aggregation processes in combination with sedimentation of clusters. More precisely, we show that the evolution equation is well-posed for a large class of coagulation kernels and output rates. Additionally, in the long-time limit we prove that solutions converge to a unique equilibrium with exponential rate under a suitable smallness condition on the coefficients.


Discrete Smoluchowski equation Coagulation Forcing Equilibrium Exponential convergence 

Mathematics Subject Classification

34A34 34D05 82C21 82C05 



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Authors and Affiliations

  1. 1.Research Unit “Multiscale and Stochastic Dynamics”, Faculty of MathematicsTechnical University of MunichGarching bei MünchenGermany
  2. 2.Departamento de Matemática Aplicada, Facultad de CienciasUniversity of GranadaGranadaSpain

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