In this paper, we prove the global in time solvability of the continuous growth–fragmentation–coagulation equation with unbounded coagulation kernels, in spaces of functions having finite moments of sufficiently high order. The main tool is the recently established result on moment regularization of the linear growth–fragmentation semigroup that allows us to consider coagulation kernels whose growth for large clusters is controlled by how good the regularization is, in a similar manner to the case when the semigroup is analytic. This article is part of the theme issue ‘Semigroup applications everywhere’.

中文翻译：

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具有无界凝固核的生长-破碎-凝固方程


在本文中，我们证明了具有无界凝结核的连续生长-破碎-凝结方程在具有足够高阶的有限矩的函数空间中的全局时间可解性。主要工具是最近建立的线性增长-分裂半群矩正则化的结果，它使我们能够考虑凝聚核，其大簇的增长由正则化的好坏控制，与半群为分析的。本文是“半群应用无处不在”主题的一部分。